tag:blogger.com,1999:blog-77216569682385269752024-03-16T12:11:35.312+11:00JPBjpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.comBlogger712125tag:blogger.com,1999:blog-7721656968238526975.post-194363617805652882024-03-09T12:18:00.105+11:002024-03-14T00:30:14.793+11:00Cover structures by base<p>In recent weeks I have been rereading the 2000s file <a href="https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=b2a493f89a58b8d9894521f6224034bb8ed1608a">‘Generalizing Sierpiński Numbers to Base <b>b</b>’</a>, written by a team from the University of Tennessee at Martin.</p><p>Although Sierpiński numbers to base 2 are well-known in studies of prime numbers because <i>Proth primes</i> — those of the form k*2<sup>n</sup>+1 — occur frequently as possible factors of binomial numbers like Mersenne and Fermat numbers, similar numbers for other bases were not studied until the 1990s. Moreover, although a major project exists to verify <a href="http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm">the smallest Sierpiński number for all bases up to 1030</a>, bases as small as 71 have not been started yet.</p><p>What was really interesting to me re-reading ‘Generalizing Sierpiński Numbers to Base <b>b</b>’ (my off-line .pdf copy is under a slightly different title but has the same text) this summer was the discussion of various covering set periods. The UT Martin team noted that different bases have vastly different minimal periods for a covering set of primes to repeat. For bases that are 2 or one fewer than a power of 2, this period is relatively long. This is because for a number of the form 2<sup>n</sup>-1 where n is any integer, b<sup>2</sup>-1 has no “primitive divisor” — that is, no prime divisor that does not divide a smaller number of the form b<sup>n</sup>-1. This is because:</p><p></p><ol style="text-align: left;"><li>b<sup>2</sup>-1 = (b+1)(b-1)</li><li>b+1 is a power of 2</li><li>both b+1 and b-1 divide by 2</li><li>so, b<sup>2</sup>-1 lacks a prime divisor for these bases</li><li>Bang’s Theorem states that the only other such case is 2<sup>6</sup>-1, which I will not discuss further</li></ol><div>The absence of a factor with period 2 means that for bases of the form 2<sup>n</sup>-1 covering sets must be built from prime numbers with longer periods. For other numbers, there will always be a cover with period 12 or shorter, but for base 3, there can be no cover repeating more frequently than every 48 terms, as was established <a href="https://www.researchgate.net/profile/Yannick-Saouter/publication/2619664_A_Fermat-Like_Sequence_and_Primes_of_the_Form_2h3n1/links/0912f50d4ca6fcd5ce000000/A-Fermat-Like-Sequence-and-Primes-of-the-Form-2h3n-1.pdf?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InB1YmxpY2F0aW9uIiwicGFnZSI6InB1YmxpY2F0aW9uIn19">by Yannick Saouter</a> in 1995.</div><div><br /></div><div>In the following table, I will indicate the presence or absence for bases from 2 to 175 of covers with the following periods:</div><div><ul style="text-align: left;"><li>2</li><li>3</li><li>4</li><li>6</li><li>8</li><li>9</li><li>10</li><li>12</li><li>15</li></ul><div>Covers with periods 5, 7, 11 and 13, as was noted by the UT Martin team, do not occur for any base so small as 175. 14-covers have not been investigated, although such a cover would be expected to involve eight primes, one with period 2 and seven with periods 7 or 14.</div><div><br /></div><div>8-, 9-, 10- and 15-covers were not discussed in the UT Martin study, although I have long known of the 8-cover {11, 73, 101, 137} in base 10. The smallest base for whcih an 8-cover provides the smallest Sierpiński number is <i>168</i>, and I know of no base where a 9-cover, 10-cover or 15-cover provide the smallest Sierpiński or Riesel number, but my re-read made me feel these were worthy of study.</div></div><div><br /></div><div>For all bases:</div><div><ul style="text-align: left;"><li><span style="color: #cc0000;">red</span> means the base lacks a cover with that period</li><li><span style="color: #93c47d;">light green</span> means a non-primitive cover</li><li><span style="color: #274e13;">dark green</span> means a primitive cover that cannot be reduced</li></ul></div><style type="text/css">
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<th class="tg-baqh" colspan="10"><span style="font-weight:bold">Presence or absence of N-cover for Bases from 2 to 175</span></th>
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<tbody>
<tr>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">N-cover</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">2</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">3</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">4</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">6</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">8</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">9</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">10</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">12</span></td>
<td class="tg-yla0"><span style="font-style:normal;text-decoration:none;color:black">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">2</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">3</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">4</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">5</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">6</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">7</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">8</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">9</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">10</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">11</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">12</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">13</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">14</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">15</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">16</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">17</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">18</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">19</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">20</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">21</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">22</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">23</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">24</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">25</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">26</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">27</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">28</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">29</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">30</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">31</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">32</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">33</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">34</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">35</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">36</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">37</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">38</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">39</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">40</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">41</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">42</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">43</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">44</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">45</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">46</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">47</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">48</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">49</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">50</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">51</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">52</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">53</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">54</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">55</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">56</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">57</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">58</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">59</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">60</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">61</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">62</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">63</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">64</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">65</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">66</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">67</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">68</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">69</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">70</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">71</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">72</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">73</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">74</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">75</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">76</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">77</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">78</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">79</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">80</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">81</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">82</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">83</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">84</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">85</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">86</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">87</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">88</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">89</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">90</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">91</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">92</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">93</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">94</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">95</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">96</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">97</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">98</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">99</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">100</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">101</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">102</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">103</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">104</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">105</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">106</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">107</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">108</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">109</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">110</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">111</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">112</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">113</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">114</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">115</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">116</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">117</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">118</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">119</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">120</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">121</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">122</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">123</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">124</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">125</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">126</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">127</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">128</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">129</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">130</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">131</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">132</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">133</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">134</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">135</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">136</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">137</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">138</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">139</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">140</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">141</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">142</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">143</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">144</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">145</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">146</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">147</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">148</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">149</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">150</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">151</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">152</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">153</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">154</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">155</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">156</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">157</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">158</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">159</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">160</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">161</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">162</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">163</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">164</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">165</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">166</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">167</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">168</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">169</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">170</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">171</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">172</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">173</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">174</span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black">175</span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-01oo"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#12501A"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
<td class="tg-6p0p"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#3C7D22"> </span></td>
<td class="tg-cbjb"><span style="font-weight:400;font-style:normal;text-decoration:none;color:black;background-color:#C00000"> </span></td>
</tr>
</tbody>
</table>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-5900342658699856372024-02-09T18:24:00.000+11:002024-02-10T01:27:51.128+11:00The amazing figures of Jack Owens in 1926 and 1930<p>Although I have ever since childhood been interested in (Australian rules) football statistics, it is only since reading the <b><u>Full Points Footy</u></b> site in the 2000s that my interest was extended beyond the VFL/AFL. Whilst I did have some background knowledge of other football competitions, it was only with <b><u>Full Points Footy</u></b> that I gained any detailed knowledge of the SANFL and WA(N)FL before the national completion began in the late 1980s.</p><p>One of the most remarkable things I discovered from reading the SANFL season scores of the middle to late 1920s was the extent to which Jack Owens monopolised scoring for Glenelg in some seasons. In his book <b><u>Goals, Goals, Goals: A Study of League and Association Full-Forwards</u></b>, Marc Fiddian paid limited attention to cases of players kicking all their team’s goals in a match, in favour of focusing on the extremely large goal tallies common in the VFA during my childhood. Nevertheless, there is an attraction to cases where one player monopolises scoring to an unusual degree — the team is totally dependent upon one player to score, and that naturally affects the attention granted to that player, and may make that player work much harder knowing that nobody else can do his job. (The phenomenon is well known to me from such county bowlers as “Tich” Freeman and George Dennett, who often took over half their team’s wickets for an entire season, feasible for a spin bowler under conditions not rigged against them by covering and “log bats”.)</p><p>Owens, who came from Broken Hill to Glenelg at a time when the club had not won a game in three seasons, would established himself very quickly around the time the club finally opened its account in the first game of 1925. He would set SA(N)FL goalkicking records — that would almost immediately be broken by North Adelaide’s Ken Farmer — in 1927 and 1928. Although Glenelg would improve substantially from their first three seasons, this improvement would during the period under discussion not be sufficient to lift them above seventh in an eight-club competition. What has attracted my attention for some years, though, is <i>the proportion of Glenelg’s goals Owens kicked</i>. The 1989 <b><u>3AW Book of Footy Records</u></b>, which I discarded many years ago, noted Ted Tyson’s goalkicking feats for the West Perth team of 1938 and 1939, who lost 27 consecutive games. Whilst these are remarkable, my study of the scores and season goalkicking figures for the SA(N)FL seasons between 1925 and 1932 shows that Owens actually surpassed Tyson’s monopolisation of the scoring. In fact, in the seasons of 1926 and 1930, Owens kicked <i>over half of all Glenelg’s goals</i>, a feat which the 2000s <b><u>AFL Record</u></b> encyclopedias show never to have been achieved over a full season in the VFL/AFL. The closest approach occurred in 1944 when Melbourne’s Fred Fanning kicked 48.33 percent of the team’s goals in the fourteen games he played. Fanning, though, missed four through suspension.</p>
<h1 style="text-align: left;">1926:</h1>
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<thead>
<tr>
<th class="tg-uzvj">Round</th>
<th class="tg-wa1i">1</th>
<th class="tg-wa1i">2</th>
<th class="tg-wa1i">3</th>
<th class="tg-wa1i">4</th>
<th class="tg-wa1i">5</th>
<th class="tg-wa1i">6</th>
<th class="tg-wa1i">7</th>
<th class="tg-wa1i">8</th>
<th class="tg-wa1i">9</th>
<th class="tg-wa1i">10</th>
<th class="tg-wa1i">11</th>
<th class="tg-wa1i">12</th>
<th class="tg-wa1i">13</th>
<th class="tg-wa1i">14</th>
<th class="tg-wa1i">Total</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-cly1" rowspan="2">Owens</td>
<td class="tg-mwxe">0</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">4</td>
<td class="tg-mwxe">6</td>
<td class="tg-mwxe">6</td>
<td class="tg-mwxe">7</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">7</td>
<td class="tg-mwxe">7</td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe">6</td>
<td class="tg-mwxe">6</td>
<td class="tg-mwxe">64</td>
</tr>
<tr>
<td class="tg-mwxe">0.00%</td>
<td class="tg-mwxe">20.00%</td>
<td class="tg-hwdb">55.56%</td>
<td class="tg-mwxe">44.44%</td>
<td class="tg-g0ak">75.00%</td>
<td class="tg-hwdb">50.00%</td>
<td class="tg-hwdb">70.00%</td>
<td class="tg-mwxe">14.29%</td>
<td class="tg-hwdb">71.43%</td>
<td class="tg-hwdb">63.64%</td>
<td class="tg-mwxe">43.75%</td>
<td class="tg-g0ak">75.00%</td>
<td class="tg-hwdb">66.67%</td>
<td class="tg-hwdb">66.67%</td>
<td class="tg-hwdb">54.24%</td>
</tr>
<tr>
<td class="tg-cly1">C. Sallis</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">12</td>
</tr>
<tr>
<td class="tg-cly1">Drew</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">8</td>
</tr>
<tr>
<td class="tg-cly1">Hack</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">4</td>
</tr>
<tr>
<td class="tg-cly1">P. Leverington</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">4</td>
</tr>
<tr>
<td class="tg-cly1">C. Hoft</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">4</td>
</tr>
<tr>
<td class="tg-cly1">Lyne</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">W. Hill</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">Gun</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">Exley</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">L. Sallis</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
</tr>
<tr>
<td class="tg-cly1">L. Leverington</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
</tr>
<tr>
<td class="tg-cly1">J. Davies</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
</tr>
<tr>
<td class="tg-cly1">Toms</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">Lloyd</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">C. Hill</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">Barbary</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-yla0">Total</td>
<td class="tg-zt7h">2</td>
<td class="tg-zt7h">5</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">8</td>
<td class="tg-zt7h">12</td>
<td class="tg-zt7h">10</td>
<td class="tg-zt7h">7</td>
<td class="tg-zt7h">7</td>
<td class="tg-zt7h">11</td>
<td class="tg-zt7h">16</td>
<td class="tg-zt7h">4</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">118</td>
</tr>
</tbody>
</table>
<h1 style="text-align: left;">1930:</h1>
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<tr>
<th class="tg-wa1i">Round</th>
<th class="tg-zt7h">1</th>
<th class="tg-zt7h">2</th>
<th class="tg-zt7h">3</th>
<th class="tg-zt7h">4</th>
<th class="tg-zt7h">5</th>
<th class="tg-zt7h">6</th>
<th class="tg-zt7h">7</th>
<th class="tg-zt7h">8</th>
<th class="tg-zt7h">9</th>
<th class="tg-zt7h">10</th>
<th class="tg-zt7h">11</th>
<th class="tg-zt7h">12</th>
<th class="tg-zt7h">13</th>
<th class="tg-zt7h">14</th>
<th class="tg-zt7h">15</th>
<th class="tg-zt7h">16</th>
<th class="tg-zt7h">17</th>
<th class="tg-wa1i">Total</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-cly1" rowspan="2">Owens</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">6</td>
<td class="tg-mwxe">4</td>
<td class="tg-mwxe">10</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">8</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">5</td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe">4</td>
<td class="tg-mwxe">10</td>
<td class="tg-mwxe">8</td>
<td class="tg-mwxe">11</td>
<td class="tg-mwxe">8</td>
<td class="tg-mwxe">99</td>
</tr>
<tr>
<td class="tg-hwdb">71.43%</td>
<td class="tg-hwdb">60.00%</td>
<td class="tg-mwxe">44.44%</td>
<td class="tg-g0ak">90.91%</td>
<td class="tg-mwxe">11.11%</td>
<td class="tg-mwxe">41.67%</td>
<td class="tg-hwdb">53.33%</td>
<td class="tg-hwdb">55.56%</td>
<td class="tg-hwdb">71.43%</td>
<td class="tg-mwxe">16.67%</td>
<td class="tg-mwxe">35.71%</td>
<td class="tg-mwxe">33.33%</td>
<td class="tg-mwxe">40.00%</td>
<td class="tg-g0ak">83.33%</td>
<td class="tg-g0ak">80.00%</td>
<td class="tg-hwdb">68.75%</td>
<td class="tg-g0ak">80.00%</td>
<td class="tg-hwdb">56.25%</td>
</tr>
<tr>
<td class="tg-cly1">Thompson</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">12</td>
</tr>
<tr>
<td class="tg-cly1">Link</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">10</td>
</tr>
<tr>
<td class="tg-cly1">Sallis</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">8</td>
</tr>
<tr>
<td class="tg-cly1">Rosewarne</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">8</td>
</tr>
<tr>
<td class="tg-cly1">Coller</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">7</td>
</tr>
<tr>
<td class="tg-cly1">Winkler</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">6</td>
</tr>
<tr>
<td class="tg-cly1">Morrow</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">Hill</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">Drew</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">Griffiths</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">K. Oliver</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe">3</td>
</tr>
<tr>
<td class="tg-cly1">Johnston</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
</tr>
<tr>
<td class="tg-cly1">Whitehead</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
</tr>
<tr>
<td class="tg-cly1">Guiney</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">2</td>
</tr>
<tr>
<td class="tg-cly1">Edwards</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">Percy</td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">Wickham</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">Lloyd</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-cly1">Wright</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe"></td>
<td class="tg-mwxe">1</td>
</tr>
<tr>
<td class="tg-yla0">Total</td>
<td class="tg-zt7h">7</td>
<td class="tg-zt7h">10</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">11</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">12</td>
<td class="tg-zt7h">15</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">7</td>
<td class="tg-zt7h">6</td>
<td class="tg-zt7h">14</td>
<td class="tg-zt7h">9</td>
<td class="tg-zt7h">10</td>
<td class="tg-zt7h">12</td>
<td class="tg-zt7h">10</td>
<td class="tg-zt7h">16</td>
<td class="tg-zt7h">10</td>
<td class="tg-zt7h">176</td>
</tr>
</tbody>
</table>From these two tables, we can see that:<div><ol style="text-align: left;"><li>in the last four games of 1930, Owens kicked <i>37 of Glenelg’s 48 goals</i> —more than 75 percent, a proportion unrivalled for so long a period</li><li>in 1926, Owens kicked at least half of Glenelg’s goals in nine of fourteen matches (64.28 percent)</li><li>in 1930, Owens kicked at least half of Glenelg’s goals in ten of seventeen matches (58.82 percent)</li></ol><div>With Tyson, John Coleman, Austin Robertson junior, Peter Hudson, Tony Lockett, and Brendan Fevola, scoring monopolisation was never as pronounced as 1), although, apart from “Ocker”, I have not thoroughly checked. It is odd that 3AW did not notice this.</div></div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-49280845144979210002023-12-10T19:31:00.002+11:002023-12-10T23:04:18.692+11:00The problem of “don’t ask” just from fearing no<p>This evening I went into a terrible temper tantrum when my mother complained that I left cooking rissoles for tonight’s dinner until they were seriously overcooked and smelling.</p><p>The tantrum, with familiar phrases (mantras) like:</p><blockquote><p style="text-align: center;">“get the word “can” out of your head”</p></blockquote><blockquote><p style="text-align: center;">“there’s no such word as “can””</p></blockquote>and less familiar mantras like<blockquote><p style="text-align: center;">“I used to be able to [remember to come down] but I can’t now”</p></blockquote>and gestures like trying to place the word “can” in the rubbish bin in the kitchen [by pointing to the rubbish bin in a terribly agitated manner], became so bad that I even walked out of the house without my mobile phone! Outside I was just as angry and agitated — trying basically to make my mother recognise that I was totally incapable of reminding myself that I had cooking to remember when I was sitting at the very computer where I am writing this post.<div><br /></div><div>My mother was just as upset as I was — and I might note that she has not been well in recent weeks, having mucus-y coughs for the past week or more. It has been difficult for me to appreciate her troubles, but I <i>hope</i> I becoming less bad at it.</div><div><br /></div><div>After I came back — deliberately knocking softly in order to, as it were, persuade my mother that I had calmed down — I did speak much more calmly about the issue. I enjoy cooking, but my mother had said that I might have to give it up if I forget it time and time again as I have been doing for the past few weeks.</div><div><br /></div><div>When I look at it logically, I recognise how I was obsessed with watching football and possessed <i>zero desire</i> to do the cooking. I simply wished to watch the football and listen to music as I had been doing for many hours before I went out to walk the dog, but feared my mother’s opinion too much to say “no”. So, I did the cooking as quickly as possible and was quite lucky in fact not to burn the spring onion, celery and mushroom mix that was to be mixed with the mince to make the rissoles. Although I said to Mummy that I would come back when I put the rissoles in the oven, I immediately and totally forgot as soon as I was back settled at the computer watching football. There was not the slightest thought about what was happening inside the oven until the DVD was finished. So unconcerned was I that I was actually <i>surprised</i> that the rissoles had nearly burned over!</div><div><br /></div><div>Once I came back, realising that I could not keep screaming and screaming outside, and even feeling my vocal cords somewhat weakened, I tried to talk to my mother about what needs to be done to give some hope this will not happen as consistently as it has been of late. I am probably reasonably convinced that there is no hope I can be instructed to remember to come down when I am totally focused on listening to music or on watching football (of course, <i>anything</i> I am watching on the computer would have the same effect as football!). Both of us were extremely upset at the way I expected my mother to be a “lackey” upon whom we can fall back whenever I forget cooking jobs that I do just to please her when my actual desire is to listen to music or watch something on the computer. I actually say I want to cook to appease my mother when I actually want to spend all day doing exactly what I want — which, today, was to watch football.</div><div><br /></div><div>However, the most notable lesson from tonight’s tempera tantrum was that my consistent refusal to ask my mother whether she would either:</div><div><ol style="text-align: left;"><li>remind me by coming up to the study or</li><li>look after my cooking</li></ol>out of fear of being told “no” is really, really bad. It might be <i>wise</i> because I know all too well that if my mother said “no” I would most likely go straight into a meltdown as bad as today’s. However, my deliberate silence has meant that my mother and I are both left ignoring the cooking with risks of burning. When I look at it, I thought of the many old English cricketers — for example Walter Brearley or George Louden — who would likely have greatly improved England’s prospects in Australia but were never questioned about touring because MCC was sufficiently aware they had zero possibility of being away from business for so long. My case is different because I have never tried — out of <i>partially</i> justifiable fear of being told “no” — to ask my mother to watch over my cooking. Instead, I assume she will do so as <i>my slave</i>. When in a tantrum, of course, I justify it as a “one-way street” where I can do and get exactly what I want one hundred percent of the time, although logically this “one-way street” is totally selfish and makes everybody else totally immaterial. It is clear to me — whether I cam capable of change or not (and I have zero belief I am) — that I must do something to prevent me forgetting my cooking, or develop some sort of compromise where I do the preparation and my mother agrees to watch over the cooking. In a logical mood these compromises are terribly unfair to my mother, but given my lack of genuine interest in cooking it is unclear what else we can do??</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-44733017789388241222023-09-05T13:22:00.057+10:002023-09-06T00:01:10.573+10:00Where there cannot be the maximum number of primes<p>In a few posts from last year, I discussed <i>pentatrigesimal</i> representation of numbers using all numbers and all letters except O (“O” being a common reading of the number “0” and very similar in shape).</p><p>One interesting discovery I made is that whilst 35 consecutive numbers can contain as many as ten primes, if we tabulate divisibility of numbers between each multiple of 35, we find something quite interesting:</p><style type="text/css">
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<table class="tg" style="table-layout: fixed; width: 462px;">
<colgroup>
<col style="width: 107px;"></col>
<col style="width: 59px;"></col>
<col style="width: 60px;"></col>
<col style="width: 59px;"></col>
<col style="width: 59px;"></col>
<col style="width: 59px;"></col>
<col style="width: 59px;"></col>
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<thead>
<tr>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">k</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">6n</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">6n+1</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">6n+2</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">6n+3</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">6n+4</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; text-decoration: none;">6n+5</span></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">A</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">B</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">C</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">D</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">E</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">F</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">G</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">H</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">I</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">J</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">K</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">L</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">M</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">N</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">P</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">Q</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">R</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">S</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">T</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">U</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">V</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">W</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">X</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">Y</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
</tr>
<tr>
<td class="tg-2b7s"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">Z</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;"> </span><br /></td>
</tr>
<tr>
<td class="tg-kex3"><b><span style="color: black; font-style: normal; text-decoration: none;">Possible primes</span></b></td>
<td class="tg-j6zm"><b><span style="color: black; font-style: normal; text-decoration: none;">8</span></b></td>
<td class="tg-j6zm"><b><span style="color: black; font-style: normal; text-decoration: none;">8</span></b></td>
<td class="tg-j6zm"><b><span style="color: black; font-style: normal; text-decoration: none;">8</span></b></td>
<td class="tg-j6zm"><b><span style="color: black; font-style: normal; text-decoration: none;">8</span></b></td>
<td class="tg-j6zm"><b><span style="color: black; font-style: normal; text-decoration: none;">8</span></b></td>
<td class="tg-j6zm"><b><span style="color: black; font-style: normal; text-decoration: none;">8</span></b></td>
</tr>
</tbody>
</table><p>
What we see is that whilst there can be ten primes in a span of thirty-five numbers, there can as shown above <i>never be more than eight primes between consecutive multiples of 35</i>. The first occurrence of eight primes between multiples of 35 is between the pentatrigesimal numbers <b>4L0</b> and <b>4LZ</b>, or in decimal 5,635 to 5,669, whereby 5,639, 5,641, 5,647, 5,651, 5,653, 5,657, 5,659 and 5,669 are all primes.</p><p>What I found reading today is that OEIS has actually tabulated the number of possible primes between multiples of base <b>b</b>, as well as the number possible in an arbitrary sequence of length <b>n</b>. I have compared “decades” and “centuries” in all bases up to 35, with sequences serving “centuries” (<b>k</b>00) shaded in grey:</p><style type="text/css">
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.tg th{border-color:black;border-style:solid;border-width:2px;font-family:Arial, sans-serif;font-size:14px;
font-weight:normal;overflow:hidden;padding:3px 5px;word-break:normal;}
.tg .tg-cly1{text-align:left;vertical-align:middle}
.tg .tg-iuxe{background-color:#A6A6A6;font-weight:bold;text-align:left;vertical-align:bottom}
.tg .tg-ti75{background-color:#A6A6A6;text-align:left;vertical-align:bottom}
.tg .tg-5g05{font-weight:bold;position:-webkit-sticky;position:sticky;text-align:left;top:-1px;vertical-align:bottom;
will-change:transform}
.tg .tg-dmes{position:-webkit-sticky;position:sticky;text-align:left;top:-1px;vertical-align:bottom;will-change:transform}
.tg .tg-7zrl{text-align:left;vertical-align:bottom}
.tg .tg-j6zm{font-weight:bold;text-align:left;vertical-align:bottom}
.tg .tg-py2d{background-color:#A6A6A6;text-align:left;vertical-align:middle}
.tg .tg-u84o{font-weight:bold;text-align:left;text-decoration:underline;vertical-align:bottom}
.tg .tg-s7xk{background-color:#A6A6A6;font-weight:bold;text-align:left;text-decoration:underline;vertical-align:bottom}
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<table class="tg" style="table-layout: fixed; width: 361px;">
<colgroup>
<col style="width: 67px;"></col>
<col style="width: 67px;"></col>
<col style="width: 72px;"></col>
<col style="width: 71px;"></col>
<col style="width: 84px;"></col>
</colgroup>
<thead>
<tr>
<th class="tg-5g05" colspan="2"><span style="color: black; font-style: normal; font-weight: bold; text-decoration: none;">Base</span></th>
<th class="tg-dmes"><span style="color: black; font-style: normal; font-weight: bold; text-decoration: none;">Arbitrary</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; font-weight: bold; text-decoration: none;">Multiple</span></th>
<th class="tg-5g05"><span style="color: black; font-style: normal; font-weight: bold; text-decoration: none;">Difference</span></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">21</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-u84o"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: underline;">-2</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">22</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">24</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">25</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">26</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">28</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">29</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">30</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">31</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-j6zm"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">32</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">33</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-u84o"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: underline;">-2</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">34</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl" colspan="2"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">35</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-u84o"><span style="color: black; font-style: normal; font-weight: 700; text-decoration: underline;">-2</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">36</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">49</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">64</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">81</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">100</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">121</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">26</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">144</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">31</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">30</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">169</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">37</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">36</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">196</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">41</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">41</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">225</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">46</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">45</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">289</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">58</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">56</span></td>
<td class="tg-s7xk"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: underline;">-2</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">324</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">62</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">62</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">361</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">68</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">67</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">400</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">75</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">75</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">21</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">441</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">81</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">80</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">22</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">484</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">88</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">87</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">529</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">95</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">94</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">24</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">576</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">101</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">101</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">25</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">625</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">109</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">109</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">26</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">676</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">117</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">116</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">729</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">124</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">124</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">28</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">784</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">132</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">131</span></td>
<td class="tg-iuxe"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: none;">-1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">29</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">841</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">141</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">139</span></td>
<td class="tg-s7xk"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: underline;">-2</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">30</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">900</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">149</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">149</span></td>
<td class="tg-ti75"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">31</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">961</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">158</span></td>
<td class="tg-py2d"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 400; text-decoration: none;">156</span></td>
<td class="tg-s7xk"><span style="background-color: #a6a6a6; color: black; font-style: normal; font-weight: 700; text-decoration: underline;">-2</span></td>
</tr>
</tbody>
</table><p>As you can see, the pentatrigesimal case I discovered earlier is not exceptional. For base 21, one already sees that there can never be more than five primes between multiples of 21, but there can be seven primes within arbitrary sequences of 21 numbers.</p><p>Nonetheless, the list is revealing because — as it did for me — it gave a false impression that there must be more prime-dense “decades” in pentatrigesimal than that from <b>4L0</b> to <b>4LZ</b> (5,635 to 5,669 in decimal). In cases like this one does need to take some care looking for prime constellations that can actually be easily proved impossible.<br /></p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-12594968685738689072023-08-29T00:28:00.103+10:002023-12-23T23:40:16.958+11:00Illustrating each count of composites not divisible by 2, 3, or 5Following on from <a href="http://jpbenney.blogspot.com/2023/08/an-alternative-view-of-primes-in.html">my previous post</a>, I will now illustrate each count of composite numbers no divisible by 2, 3, or 5 in a century, except for those not known to occur.<div><br /></div><div>Some of these tables have been shown on this blog at <a href="http://jpbenney.blogspot.com/2014/05/the-16719th-century-and-other-prime.html">‘The 16,719th century and other prime-free sequences’</a> from almost a decade ago.</div><div><br /></div><div>For a few counts affected by the “eight-digit gap” — those from nine to eleven — I will show those centuries immediately below and above the “eight-digit gap” in a subsequent table for more perspective. Centuries with fewer than nine composites not divisible by 2, 3, or 5 also show the effect of the “eight-digit gap”, but this is obscured because no century below the eight-digit gap has six or eight composites not divisible by 2, 3, or 5, whilst none with seven larger than the second century are known — and of course none wiht the theoretically possible four or five composites not divisible by 2, 3, or 5 have yet been found.
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<table class="tg">
<thead>
<tr>
<th class="tg-wa1i">n</th>
<th class="tg-1wig">Factorisations of numbers not divisible by 2, 3, or 5</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-nrix">3</td>
<td class="tg-9iv7">7 is prime<br />11 is prime<br />13 is prime<br />17 is prime<br />19 is prime<br />23 is prime<br />29 is prime<br />31 is prime<br />37 is prime<br />41 is prime<br />43 is prime<br />47 is prime<br /><span style="color: red;">1. 49 = 7 × 7</span><br />53 is prime<br />59 is prime<br />61 is prime<br />67 is prime<br />71 is prime<br />73 is prime<br /><span style="color: red;">2. 77 = 7 × 11</span><br />79 is prime<br />83 is prime<br />89 is prime<br /><span style="color: red;">3. 91 = 7 × 13</span><br /><span style="font-style: normal; font-weight: 400; text-decoration: none;">97 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">4</td>
<td class="tg-0lax">(none known)</td>
</tr>
<tr>
<td class="tg-nrix">5</td>
<td class="tg-0lax">(none known)</td>
</tr>
<tr>
<td class="tg-nrix">6</td>
<td class="tg-0lax">39433867730216371575457664401 is prime<br />39433867730216371575457664407 is prime<br />39433867730216371575457664411 is prime<br />39433867730216371575457664413 is prime<br />39433867730216371575457664417 is prime<br /><span style="color: red;">1. 39433867730216371575457664419 = 7 × 19 × 23 × 229 × 2179 × 25834328988233247551</span><br />39433867730216371575457664423 is prime<br />39433867730216371575457664429 is prime<br />39433867730216371575457664431 is prime<br />39433867730216371575457664437 is prime<br />39433867730216371575457664441 is prime<br />39433867730216371575457664443 is prime<br /><span style="color: red;">2. 39433867730216371575457664447 = 7 × 11 × 29 × 993961 × 17766885682653834719</span><br />39433867730216371575457664449 is prime<br />39433867730216371575457664453 is prime<br />39433867730216371575457664459 is prime<br /><span style="color: red;">3. 39433867730216371575457664461 = 7 × 13 × 233 × 6050207 × 307398559703912641</span><br />39433867730216371575457664467 is prime<br />39433867730216371575457664471 is prime<br />39433867730216371575457664473 is prime<br />39433867730216371575457664477 is prime<br />39433867730216371575457664479 is prime<br />39433867730216371575457664483 is prime<br /><span style="color: red;">4. 39433867730216371575457664489 = 7 × 17 × 9470228338819 × 34991451936949</span><br /><span style="color: red;">5. 39433867730216371575457664491 = 11 × 47 × 432569 × 331736687 × 531532637641</span><br /><span style="font-style: normal; font-weight: 400; text-decoration: none;"><span style="color: red;">6. 39433867730216371575457664497 = 389 × 547968840241 × 184996669834253</span></span></td>
</tr>
<tr>
<td class="tg-nrix">7</td>
<td class="tg-0lax"><span style="color: black;">101 is prime</span><br /><span style="color: black;">103 is prime</span><br /><span style="color: black;">107 is prime</span><br /><span style="color: black;">109 is prime</span><br /><span style="color: black;">113 is prime</span><br /><span style="color: red;">1. 119 = 7 × 17</span><br /><span style="color: red;">2. 121 = 11 × 11</span><br /><span style="color: black;">127 is prime</span><br /><span style="color: black;">131 is prime</span><br /><span style="color: red;">3. 133 = 7 × 19</span><br /><span style="color: black;">137 is prime</span><br /><span style="color: black;">139 is prime</span><br /><span style="color: red;">4. 143 = 11 × 13</span><br /><span style="color: black;">149 is prime</span><br /><span style="color: black;">151 is prime</span><br /><span style="color: black;">157 is prime</span><br /><span style="color: red;">5. 161 = 7 × 23</span><br /><span style="color: black;">163 is prime</span><br /><span style="color: black;">167 is prime</span><br /><span style="color: red;">6. 169 = 13 × 13</span><br /><span style="color: black;">173 is prime</span><br /><span style="color: black;">179 is prime</span><br /><span style="color: black;">181 is prime</span><br /><span style="color: red;">7. 187 = 11 × 17</span><br /><span style="color: black;">191 is prime</span><br /><span style="color: black;">193 is prime</span><br /><span style="color: black;">197 is prime</span><br /><span style="color: black;">199 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">8</td>
<td class="tg-0lax"><span style="color: black;">2335286971401803 is prime</span><br /><span style="color: black;">2335286971401809 is prime</span><br /><span style="color: red;">1. 2335286971401811 = 7 × 137 × 9433 × 258149813</span><br /><span style="color: red;">2. 2335286971401817 = 37 × 89 × 257 × 1319 × 2092043</span><br /><span style="color: black;">2335286971401821 is prime</span><br /><span style="color: black;">2335286971401823 is prime</span><br /><span style="color: black;">2335286971401827 is prime</span><br /><span style="color: black;">2335286971401829 is prime</span><br /><span style="color: red;">3. 2335286971401833 = 83</span> <span style="color: red;">× 83</span> <span style="color: red;">× 409 × 2153 × 384961</span><br /><span style="color: red;">4. 2335286971401839 = 7 × 7</span> <span style="color: red;">× 13 × 17 × 29 × 41 × 47 × 313 × 12329</span><br /><span style="color: black;">2335286971401841 is prime</span><br /><span style="color: black;">2335286971401847 is prime</span><br /><span style="color: black;">2335286971401851 is prime</span><br /><span style="color: red;">5. 2335286971401853 = 7 × 79 × 5413 × 26711 × 29207</span><br /><span style="color: red;">6. 2335286971401857 = 11 × 127 × 1671644217181</span><br /><span style="color: black;">2335286971401859 is prime</span><br /><span style="color: black;">2335286971401863 is prime</span><br /><span style="color: black;">2335286971401869 is prime</span><br /><span style="color: black;">2335286971401871 is prime</span><br /><span style="color: black;">2335286971401877 is prime</span><br /><span style="color: red;">7. 2335286971401881 = 7 × 19 × 125507</span> <span style="color: red;">× 139900951</span> <br /><span style="color: black;">2335286971401883 is prime</span><br /><span style="color: black;">2335286971401887 is prime</span><br /><span style="color: black;">2335286971401889 is prime</span><br /><span style="color: red;">8. 2335286971401893 = 35255371</span> <span style="color: red;">× 66239183</span> <br /><span style="color: black;">2335286971401899 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">9</td>
<td class="tg-bxdl"><span style="color: red;">1. 1403 = 23 × 61</span><br /><span style="color: black;">1409 is prime</span><br /><span style="color: red;">2. 1411 = 17 × 83</span><br /><span style="color: red;">3. 1417 = 13 × 109</span><br /><span style="color: red;">4. 1421 = 7</span> <span style="color: red;">× 7</span> <span style="color: red;">× 29</span><br /><span style="color: black;">1423 is prime</span><br /><span style="color: black;">1427 is prime</span><br /><span style="color: black;">1429 is prime</span><br /><span style="color: black;">1433 is prime</span><br /><span style="color: black;">1439 is prime</span><br /><span style="color: red;">5. 1441 = 11 × 131</span><br /><span style="color: black;">1447 is prime</span><br /><span style="color: black;">1451 is prime</span><br /><span style="color: black;">1453 is prime</span><br /><span style="color: red;">6. 1457 = 31 × 47</span><br /><span style="color: black;">1459 is prime</span><br /><span style="color: red;">7. 1463 = 7 × 11 × 19</span><br /><span style="color: red;">8. 1469 = 13 × 113</span><br /><span style="color: black;">1471 is prime</span><br /><span style="color: red;">9. 1477 = 7 × 211</span><br /><span style="color: black;">1481 is prime</span><br /><span style="color: black;">1483 is prime</span><br /><span style="color: black;">1487 is prime</span><br /><span style="color: black;">1489 is prime</span><br /><span style="color: black;">1493 is prime</span><br /><span style="color: black;">1499 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">10</td>
<td class="tg-bxdl"><span style="color: red;">1. 203 = 7 × 29</span><br /><span style="color: red;">2. 209 = 11 × 19</span><br /><span style="color: black;">211 is prime</span><br /><span style="color: red;">3. 217 = 7 × 31</span><br /><span style="color: red;">4. 221 = 13 × 17</span><br /><span style="color: black;">223 is prime</span><br /><span style="color: black;">227 is prime</span><br /><span style="color: black;">229 is prime</span><br /><span style="color: black;">233 is prime</span><br /><span style="color: black;">239 is prime</span><br /><span style="color: black;">241 is prime</span><br /><span style="color: red;">5. 247 = 13 × 19</span><br /><span style="color: black;">251 is prime</span><br /><span style="color: red;">6. 253 = 11 × 23</span><br /><span style="color: black;">257 is prime</span><br /><span style="color: red;">7. 259 = 7 × 37</span><br /><span style="color: black;">263 is prime</span><br /><span style="color: black;">269 is prime</span><br /><span style="color: black;">271 is prime</span><br /><span style="color: black;">277 is prime</span><br /><span style="color: black;">281 is prime</span><br /><span style="color: black;">283 is prime</span><br /><span style="color: red;">8. 287 = 7 × 41</span><br /><span style="color: red;">9. 289 = 17 × 17</span><br /><span style="color: black;">293 is prime</span><br /><span style="color: red;">10. 299 = 13 × 23</span></td>
</tr>
<tr>
<td class="tg-nrix">11</td>
<td class="tg-0lax"><span style="color: black;">401 is prime</span><br /><span style="color: red;">1. 403 = 13 × 31</span><br /><span style="color: red;">2. 407 = 11 × 37</span><br /><span style="color: black;">409 is prime</span><br /><span style="color: red;">3. 413 = 7 × 59</span><br /><span style="color: black;">419 is prime</span><br /><span style="color: black;">421 is prime</span><br /><span style="color: red;">4. 427 = 7 × 61</span><br /><span style="color: black;">431 is prime</span><br /><span style="color: black;">433 is prime</span><br /><span style="color: red;">5. 437 = 19 × 23</span><br /><span style="color: black;">439 is prime</span><br /><span style="color: black;">443 is prime</span><br /><span style="color: black;">449 is prime</span><br /><span style="color: red;">6. 451 = 11 × 41</span><br /><span style="color: black;">457 is prime</span><br /><span style="color: black;">461 is prime</span><br /><span style="color: black;">463 is prime</span><br /><span style="color: black;">467 is prime</span><br /><span style="color: red;">7. 469 = 7 × 67</span><br /><span style="color: red;">8. 473 = 11 × 43</span><br /><span style="color: black;">479 is prime</span><br /><span style="color: red;">9. 481 = 13 × 37</span><br /><span style="color: black;">487 is prime</span><br /><span style="color: black;">491 is prime</span><br /><span style="color: red;">10. 493 = 17 × 29</span><br /><span style="color: red;">11. 497 = 7 × 71</span><br /><span style="color: black;">499 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">12</td>
<td class="tg-0lax"><span style="color: black;">503 is prime</span><br /><span style="color: black;">509 is prime</span><br /><span style="color: red;">1. 511 = 7 × 73</span><br /><span style="color: red;">2. 517 = 11 × 47</span><br /><span style="color: black;">521 is prime</span><br /><span style="color: black;">523 is prime</span><br /><span style="color: red;">3. 527 = 17 × 31</span><br /><span style="color: red;">4. 529 = 23 × 23</span><br /><span style="color: red;">5. 533 = 13 × 41</span><br /><span style="color: red;">6. 539 = 7 × 7</span> <span style="color: red;">× 11</span><br /><span style="color: black;">541 is prime</span><br /><span style="color: black;">547 is prime</span><br /><span style="color: red;">7. 551 = 19 × 29</span><br /><span style="color: red;">8. 553 = 7 × 79</span><br /><span style="color: black;">557 is prime</span><br /><span style="color: red;">9. 559 = 13 × 43</span><br /><span style="color: black;">563 is prime</span><br /><span style="color: black;">569 is prime</span><br /><span style="color: black;">571 is prime</span><br /><span style="color: black;">577 is prime</span><br /><span style="color: red;">10. 581 = 7 × 83</span><br /><span style="color: red;">11. 583 = 11 × 53</span><br /><span style="color: black;">587 is prime</span><br /><span style="color: red;">12. 589 = 19 × 31</span><br /><span style="color: black;">593 is prime</span><br /><span style="color: black;">599 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">13</td>
<td class="tg-0lax"><span style="color: black;">1601 is prime</span><br /><span style="color: red;">1. 1603 = 7 × 229</span><br /><span style="color: black;">1607 is prime</span><br /><span style="color: black;">1609 is prime</span><br /><span style="color: black;">1613 is prime</span><br /><span style="color: black;">1619 is prime</span><br /><span style="color: black;">1621 is prime</span><br /><span style="color: black;">1627 is prime</span><br /><span style="color: red;">2. 1631 = 7 × 233</span><br /><span style="color: red;">3. 1633 = 23 × 71</span><br /><span style="color: black;">1637 is prime</span><br /><span style="color: red;">4. 1639 = 11 × 149</span><br /><span style="color: red;">5. 1643 = 31 × 53</span><br /><span style="color: red;">6. 1649 = 17 × 97</span><br /><span style="color: red;">7. 1651 = 13 × 127</span><br /><span style="color: black;">1657 is prime</span><br /><span style="color: red;">8. 1661 = 11 × 151</span><br /><span style="color: black;">1663 is prime</span><br /><span style="color: black;">1667 is prime</span><br /><span style="color: black;">1669 is prime</span><br /><span style="color: red;">9. 1673 = 7 × 239</span><br /><span style="color: red;">10. 1679 = 23 × 73</span><br /><span style="color: red;">11. 1681 = 41 × 41</span><br /><span style="color: red;">12. 1687 = 7 × 241</span><br /><span style="color: red;">13. 1691 = 19 × 89</span><br /><span style="color: black;">1693 is prime</span><br /><span style="color: black;">1697 is prime</span><br /><span style="color: black;">1699 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">14</td>
<td class="tg-0lax"><span style="color: black;">701 is prime</span><br /><span style="color: red;">1. 703 = 19 × 37</span><br /><span style="color: red;">2. 707 = 7 × 101</span><br /><span style="color: black;">709 is prime</span><br /><span style="color: red;">3. 713 = 23 × 31</span><br /><span style="color: black;">719 is prime</span><br /><span style="color: red;">4. 721 = 7 × 103</span><br /><span style="color: black;">727 is prime</span><br /><span style="color: red;">5. 731 = 17 × 43</span><br /><span style="color: black;">733 is prime</span><br /><span style="color: red;">6. 737 = 11 × 67</span><br /><span style="color: black;">739 is prime</span><br /><span style="color: black;">743 is prime</span><br /><span style="color: red;">7. 749 = 7 × 107</span><br /><span style="color: black;">751 is prime</span><br /><span style="color: black;">757 is prime</span><br /><span style="color: black;">761 is prime</span><br /><span style="color: red;">8. 763 = 7 × 109</span><br /><span style="color: red;">9. 767 = 13 × 59</span><br /><span style="color: black;">769 is prime</span><br /><span style="color: black;">773 is prime</span><br /><span style="color: red;">10. 779 = 19 × 41</span><br /><span style="color: red;">11. 781 = 11 × 71</span><br /><span style="color: black;">787 is prime</span><br /><span style="color: red;">12. 791 = 7 × 113</span><br /><span style="color: red;">13. 793 = 13 × 61</span><br /><span style="color: black;">797 is prime</span><br /><span style="color: red;">14. 799 = 17 × 47</span></td>
</tr>
<tr>
<td class="tg-nrix">15</td>
<td class="tg-0lax"><span style="color: black;">1901 is prime</span><br /><span style="color: red;">1. 1903 = 11 × 173</span><br /><span style="color: black;">1907 is prime</span><br /><span style="color: red;">2. 1909 = 23 × 83</span><br /><span style="color: black;">1913 is prime</span><br /><span style="color: red;">3. 1919 = 19 × 101</span><br /><span style="color: red;">4. 1921 = 17 × 113</span><br /><span style="color: red;">5. 1927 = 41 × 47</span><br /><span style="color: black;">1931 is prime</span><br /><span style="color: black;">1933 is prime</span><br /><span style="color: red;">6. 1937 = 13 × 149</span><br /><span style="color: red;">7. 1939 = 7 × 277</span><br /><span style="color: red;">8. 1943 = 29 × 67</span><br /><span style="color: black;">1949 is prime</span><br /><span style="color: black;">1951 is prime</span><br /><span style="color: red;">9. 1957 = 19 × 103</span><br /><span style="color: red;">10. 1961 = 37 × 53</span><br /><span style="color: red;">11. 1963 = 13 × 151</span><br /><span style="color: red;">12. 1967 = 7 × 281</span><br /><span style="color: red;">13. 1969 = 11 × 179</span><br /><span style="color: black;">1973 is prime</span><br /><span style="color: black;">1979 is prime</span><br /><span style="color: red;">14. 1981 = 7 × 283</span><br /><span style="color: black;">1987 is prime</span><br /><span style="color: red;">15. 1991 = 11 × 181</span><br /><span style="color: black;">1993 is prime</span><br /><span style="color: black;">1997 is prime</span><br /><span style="color: black;">1999 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">16</td>
<td class="tg-bxdl"><span style="color: red;">1. 2101 = 11 × 191</span><br /><span style="color: red;">2. 2107 = 7 ×</span> <span style="color: red;">7 × 43</span><br /><span style="color: black;">2111 is prime</span><br /><span style="color: black;">2113 is prime</span><br /><span style="color: red;">3. 2117 = 29 × 73</span><br /><span style="color: red;">4. 2119 = 13 × 163</span><br /><span style="color: red;">5. 2123 = 11 × 193</span><br /><span style="color: black;">2129 is prime</span><br /><span style="color: black;">2131 is prime</span><br /><span style="color: black;">2137 is prime</span><br /><span style="color: black;">2141 is prime</span><br /><span style="color: black;">2143 is prime</span><br /><span style="color: red;">6. 2147 = 19 × 113</span><br /><span style="color: red;">7. 2149 = 7 × 307</span><br /><span style="color: black;">2153 is prime</span><br /><span style="color: red;">8. 2159 = 17 × 127</span><br /><span style="color: black;">2161 is prime</span><br /><span style="color: red;">9. 2167 = 11 × 197</span><br /><span style="color: red;">10. 2171 = 13 × 167</span><br /><span style="color: red;">11. 2173 = 41 × 53</span><br /><span style="color: red;">12. 2177 = 7 × 311</span><br /><span style="color: black;">2179 is prime</span><br /><span style="color: red;">13. 2183 = 37 × 59</span><br /><span style="color: red;">14. 2189 = 11 × 199</span><br /><span style="color: red;">15. 2191 = 7 × 313</span><br /><span style="color: red;">16. 2197 = 13 × 13 × 13</span></td>
</tr>
<tr>
<td class="tg-nrix">17</td>
<td class="tg-0lax"><span style="color: black;">1301 is prime</span><br /><span style="color: black;">1303 is prime</span><br /><span style="color: black;">1307 is prime</span><br /><span style="color: red;">1. 1309 = 7 × 11 × 17</span><br /><span style="color: red;">2. 1313 = 13 × 101</span><br /><span style="color: black;">1319 is prime</span><br /><span style="color: black;">1321 is prime</span><br /><span style="color: black;">1327 is prime</span><br /><span style="color: red;">3. 1331 = 11 × 11 × 11</span><br /><span style="color: red;">4. 1333 = 31 × 43</span><br /><span style="color: red;">5. 1337 = 7 × 191</span><br /><span style="color: red;">6. 1339 = 13 × 103</span><br /><span style="color: red;">7. 1343 = 17 × 79</span><br /><span style="color: red;">8. 1349 = 19 × 71</span><br /><span style="color: red;">9. 1351 = 7 × 193</span><br /><span style="color: red;">10. 1357 = 23 × 59</span><br /><span style="color: black;">1361 is prime</span><br /><span style="color: red;">11. 1363 = 29 × 47</span><br /><span style="color: black;">1367 is prime</span><br /><span style="color: red;">12. 1369 = 37 × 37</span><br /><span style="color: black;">1373 is prime</span><br /><span style="color: red;">13. 1379 = 7 × 197</span><br /><span style="color: black;">1381 is prime</span><br /><span style="color: red;">14. 1387 = 19 × 73</span><br /><span style="color: red;">15. 1391 = 13 × 107</span><br /><span style="color: red;">16. 1393 = 7 × 199</span><br /><span style="color: red;">17. 1397 = 11 × 127</span><br /><span style="color: black;">1399 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix">18</td>
<td class="tg-bxdl"><span style="color: red;">1. 3101 = 7 × 443</span><br /><span style="color: red;">2. 3103 = 29 × 107</span><br /><span style="color: red;">3. 3107 = 13 × 239</span><br /><span style="color: black;">3109 is prime</span><br /><span style="color: red;">4. 3113 = 11 × 283</span><br /><span style="color: black;">3119 is prime</span><br /><span style="color: black;">3121 is prime</span><br /><span style="color: red;">5. 3127 = 53 × 59</span><br /><span style="color: red;">6. 3131 = 31 × 101</span><br /><span style="color: red;">7. 3133 = 13 × 241</span><br /><span style="color: black;">3137 is prime</span><br /><span style="color: red;">8. 3139 = 43 × 73</span><br /><span style="color: red;">9. 3143 = 7 × 449</span><br /><span style="color: red;">10. 3149 = 47 × 67</span><br /><span style="color: red;">11. 3151 = 23 × 137</span><br /><span style="color: red;">12. 3157 = 7 × 11 × 41</span><br /><span style="color: red;">13. 3161 = 29 × 109</span><br /><span style="color: black;">3163 is prime</span><br /><span style="color: black;">3167 is prime</span><br /><span style="color: black;">3169 is prime</span><br /><span style="color: red;">14. 3173 = 19 × 167</span><br /><span style="color: red;">15. 3179 = 11 × 17 × 17</span><br /><span style="color: black;">3181 is prime</span><br /><span style="color: black;">3187 is prime</span><br /><span style="color: black;">3191 is prime</span><br /><span style="color: red;">16. 3193 = 31 × 103</span><br /><span style="color: red;">17. 3197 = 23 × 139</span><br /><span style="color: red;">18. 3199 = 7 × 457</span></td>
</tr>
<tr>
<td class="tg-nrix">19</td>
<td class="tg-bxdl"><span style="color: red;">1. 4301 = 11 × 17 × 23</span><br /><span style="color: red;">2. 4303 = 13 × 331</span><br /><span style="color: red;">3. 4307 = 59 × 73</span><br /><span style="color: red;">4. 4309 = 31 × 139</span><br /><span style="color: red;">5. 4313 = 19 × 227</span><br /><span style="color: red;">6. 4319 = 7 × 617</span><br /><span style="color: red;">7. 4321 = 29 × 149</span><br /><span style="color: black;">4327 is prime</span><br /><span style="color: red;">8. 4331 = 61 × 71</span><br /><span style="color: red;">9. 4333 = 7 × 619</span><br /><span style="color: black;">4337 is prime</span><br /><span style="color: black;">4339 is prime</span><br /><span style="color: red;">10. 4343 = 43 × 101</span><br /><span style="color: black;">4349 is prime</span><br /><span style="color: red;">11. 4351 = 19 × 229</span><br /><span style="color: black;">4357 is prime</span><br /><span style="color: red;">12. 4361 = 7 × 7</span> <span style="color: red;">× 89</span><br /><span style="color: black;">4363 is prime</span><br /><span style="color: red;">13. 4367 = 11 × 397</span><br /><span style="color: red;">14. 4369 = 17 × 257</span><br /><span style="color: black;">4373 is prime</span><br /><span style="color: red;">15. 4379 = 29 × 151</span><br /><span style="color: red;">16. 4381 = 13 × 337</span><br /><span style="color: red;">17. 4387 = 41 × 107</span><br /><span style="color: black;">4391 is prime</span><br /><span style="color: red;">18. 4393 = 23 × 191</span><br /><span style="color: black;">4397 is prime</span><br /><span style="color: red;">19. 4399 = 53 × 83</span></td>
</tr>
<tr>
<td class="tg-nrix">20</td>
<td class="tg-bxdl"><span style="color: red;">1. 6401 = 37 × 173</span><br /><span style="color: red;">2. 6403 = 19 × 337</span><br /><span style="color: red;">3. 6407 = 43 × 149</span><br /><span style="color: red;">4. 6409 = 13 × 17 × 29</span><br /><span style="color: red;">5. 6413 = 11 × 11</span> <span style="color: red;">× 53</span><br /><span style="color: red;">6. 6419 = 7 × 7</span> <span style="color: red;">× 131</span><br /><span style="color: black;">6421 is prime</span><br /><span style="color: black;">6427 is prime</span><br /><span style="color: red;">7. 6431 = 59 × 109</span><br /><span style="color: red;">8. 6433 = 7 × 919</span><br /><span style="color: red;">9. 6437 = 41 × 157</span><br /><span style="color: red;">10. 6439 = 47 × 137</span><br /><span style="color: red;">11. 6443 = 17 × 379</span><br /><span style="color: black;">6449 is prime</span><br /><span style="color: black;">6451 is prime</span><br /><span style="color: red;">12. 6457 = 11 × 587</span><br /><span style="color: red;">13. 6461 = 7 × 13 × 71</span><br /><span style="color: red;">14. 6463 = 23 × 281</span><br /><span style="color: red;">15. 6467 = 29 × 223</span><br /><span style="color: black;">6469 is prime</span><br /><span style="color: black;">6473 is prime</span><br /><span style="color: red;">16. 6479 = 11 × 19 × 31</span><br /><span style="color: black;">6481 is prime</span><br /><span style="color: red;">17. 6487 = 13 × 499</span><br /><span style="color: black;">6491 is prime</span><br /><span style="color: red;">18. 6493 = 43 × 151</span><br /><span style="color: red;">19. 6497 = 73 × 89</span><br /><span style="color: red;">20. 6499 = 67 × 97</span></td>
</tr>
<tr>
<td class="tg-nrix">21</td>
<td class="tg-bxdl"><span style="color: red;">1. 14201 = 11 × 1291</span><br /><span style="color: red;">2. 14203 = 7 × 2029</span><br /><span style="color: black;">14207 is prime</span><br /><span style="color: red;">3. 14209 = 13 × 1093</span><br /><span style="color: red;">4. 14213 = 61 × 233</span><br /><span style="color: red;">5. 14219 = 59 × 241</span><br /><span style="color: black;">14221 is prime</span><br /><span style="color: red;">6. 14227 = 41 × 347</span><br /><span style="color: red;">7. 14231 = 7 × 19 × 107</span><br /><span style="color: red;">8. 14233 = 43 × 331</span><br /><span style="color: red;">9. 14237 = 23 × 619</span><br /><span style="color: red;">10. 14239 = 29 × 491</span><br /><span style="color: black;">14243 is prime</span><br /><span style="color: black;">14249 is prime</span><br /><span style="color: black;">14251 is prime</span><br /><span style="color: red;">11. 14257 = 53 × 269</span><br /><span style="color: red;">12. 14261 = 13 × 1097</span><br /><span style="color: red;">13. 14263 = 17 × 839</span><br /><span style="color: red;">14. 14267 = 11 × 1297</span><br /><span style="color: red;">15. 14269 = 19 × 751</span><br /><span style="color: red;">16. 14273 = 7 × 2039</span><br /><span style="color: red;">17. 14279 = 109 × 131</span><br /><span style="color: black;">14281 is prime</span><br /><span style="color: red;">18. 14287 = 7 × 13 × 157</span><br /><span style="color: red;">19. 14291 = 31 × 461</span><br /><span style="color: black;">14293 is prime</span><br /><span style="color: red;">20. 14297 = 17 × 29 × 29</span><br /><span style="color: red;">21. 14299 = 79 × 181</span></td>
</tr>
<tr>
<td class="tg-nrix">22</td>
<td class="tg-bxdl"><span style="color: red;">1. 31403 = 31 × 1013</span><br /><span style="color: red;">2. 31409 = 7 × 7</span> <span style="color: red;">× 641</span><br /><span style="color: red;">3. 31411 = 101 × 311</span><br /><span style="color: red;">4. 31417 = 89 × 353</span><br /><span style="color: red;">5. 31421 = 13 × 2417</span><br /><span style="color: red;">6. 31423 = 7 × 67 × 67</span><br /><span style="color: red;">7. 31427 = 11 × 2857</span><br /><span style="color: red;">8. 31429 = 53 × 593</span><br /><span style="color: red;">9. 31433 = 17 × 43 × 43</span><br /><span style="color: red;">10. 31439 = 149 × 211</span><br /><span style="color: red;">11. 31441 = 23 × 1367</span><br /><span style="color: red;">12. 31447 = 13 × 41 × 59</span><br /><span style="color: red;">13. 31451 = 7 × 4493</span><br /><span style="color: red;">14. 31453 = 71 × 443</span><br /><span style="color: red;">15. 31457 = 83 × 379</span><br /><span style="color: red;">16. 31459 = 163 × 193</span><br /><span style="color: red;">17. 31463 = 73 × 431</span><br /><span style="color: black;">31469 is prime</span><br /><span style="color: red;">18. 31471 = 11 × 2861</span><br /><span style="color: black;">31477 is prime</span><br /><span style="color: black;">31481 is prime</span><br /><span style="color: red;">19. 31483 = 19 × 1657</span><br /><span style="color: red;">20. 31487 = 23 × 37 × 37</span><br /><span style="color: black;">31489 is prime</span><br /><span style="color: red;">21. 31493 = 7 × 11 × 409</span><br /><span style="color: red;">22. 31499 = 13 × 2423</span></td>
</tr>
<tr>
<td class="tg-nrix">23</td>
<td class="tg-bxdl"><span style="color: red;">1. 40301 = 191 × 211</span><br /><span style="color: red;">2. 40303 = 41 × 983</span><br /><span style="color: red;">3. 40307 = 17 × 2371</span><br /><span style="color: red;">4. 40309 = 173 × 233</span><br /><span style="color: red;">5. 40313 = 7 × 13 × 443</span><br /><span style="color: red;">6. 40319 = 23 × 1753</span><br /><span style="color: red;">7. 40321 = 61 × 661</span><br /><span style="color: red;">8. 40327 = 7 × 7</span> <span style="color: red;">× 823</span><br /><span style="color: red;">9. 40331 = 31 × 1301</span><br /><span style="color: red;">10. 40333 = 53 × 761</span><br /><span style="color: red;">11. 40337 = 11 × 19 × 193</span><br /><span style="color: red;">12. 40339 = 13 × 29 × 107</span><br /><span style="color: black;">40343 is prime</span><br /><span style="color: red;">13. 40349 = 157 × 257</span><br /><span style="color: black;">40351 is prime</span><br /><span style="color: black;">40357 is prime</span><br /><span style="color: black;">40361 is prime</span><br /><span style="color: red;">14. 40363 = 181 × 223</span><br /><span style="color: red;">15. 40367 = 37 × 1091</span><br /><span style="color: red;">16. 40369 = 7 × 73 × 79</span><br /><span style="color: red;">17. 40373 = 47 × 859</span><br /><span style="color: red;">18. 40379 = 149 × 271</span><br /><span style="color: red;">19. 40381 = 11 × 3671</span><br /><span style="color: black;">40387 is prime</span><br /><span style="color: red;">20. 40391 = 13 × 13</span> <span style="color: red;">× 239</span><br /><span style="color: red;">21. 40393 = 31 × 1303</span><br /><span style="color: red;">22. 40397 = 7 × 29 × 199</span><br /><span style="color: red;">23. 40399 = 71 × 569</span></td>
</tr>
<tr>
<td class="tg-nrix">24</td>
<td class="tg-bxdl"><span style="color: red;">1. 180101 = 19 × 9479</span><br /><span style="color: red;">2. 180103 = 7 × 11 × 2339</span><br /><span style="color: red;">3. 180107 = 389 × 463</span><br /><span style="color: red;">4. 180109 = 233 × 773</span><br /><span style="color: red;">5. 180113 = 23 × 41 × 191</span><br /><span style="color: red;">6. 180119 = 29 × 6211</span><br /><span style="color: red;">7. 180121 = 281 × 641</span><br /><span style="color: red;">8. 180127 = 43 × 59 × 71</span><br /><span style="color: red;">9. 180131 = 7 × 25733</span><br /><span style="color: red;">10. 180133 = 61 × 2953</span><br /><span style="color: black;">180137 is prime</span><br /><span style="color: red;">11. 180139 = 19</span> <span style="color: red;">× 19</span> <span style="color: red;">× 499</span><br /><span style="color: red;">12. 180143 = 151 × 1193</span><br /><span style="color: red;">13. 180149 = 17 × 10597</span><br /><span style="color: red;">14. 180151 = 47 × 3833</span><br /><span style="color: red;">15. 180157 = 257 × 701</span><br /><span style="color: black;">180161 is prime</span><br /><span style="color: red;">16. 180163 = 67 × 2689</span><br /><span style="color: red;">17. 180167 = 13 × 13859</span><br /><span style="color: red;">18. 180169 = 11 × 11</span> <span style="color: red;">× 1489</span><br /><span style="color: red;">19. 180173 = 7 × 7</span> <span style="color: red;">× 3677</span><br /><span style="color: black;">180179 is prime</span><br /><span style="color: black;">180181 is prime</span><br /><span style="color: red;">20. 180187 = 7 × 25741</span><br /><span style="color: red;">21. 180191 = 11 × 16381</span><br /><span style="color: red;">22. 180193 = 13 × 83 × 167</span><br /><span style="color: red;">23. 180197 = 367 × 491</span><br /><span style="color: red;">24. 180199 = 79 × 2281</span></td>
</tr>
<tr>
<td class="tg-nrix">25</td>
<td class="tg-bxdl"><span style="color: red;">1. 155903 = 11 × 14173</span><br /><span style="color: red;">2. 155909 = 13 × 67 × 179</span><br /><span style="color: red;">3. 155911 = 7 × 22273</span><br /><span style="color: red;">4. 155917 = 23 × 6779</span><br /><span style="color: black;">155921 is prime</span><br /><span style="color: red;">5. 155923 = 41 × 3803</span><br /><span style="color: red;">6. 155927 = 241 × 647</span><br /><span style="color: red;">7. 155929 = 211 × 739</span><br /><span style="color: red;">8. 155933 = 19 × 29 × 283</span><br /><span style="color: red;">9. 155939 = 7 × 22277</span><br /><span style="color: red;">10 .155941 = 17 × 9173</span><br /><span style="color: red;">11. 155947 = 11 × 14177</span><br /><span style="color: red;">12. 155951 = 277 × 563</span><br /><span style="color: red;">13. 155953 = 7 × 22279</span><br /><span style="color: red;">14. 155957 = 83 × 1879</span><br /><span style="color: red;">15. 155959 = 263 × 593</span><br /><span style="color: red;">16. 155963 = 23 × 6781</span><br /><span style="color: red;">17. 155969 = 11</span> <span style="color: red;">× 11 × 1289</span><br /><span style="color: red;">18. 155971 = 19 × 8209</span><br /><span style="color: red;">19. 155977 = 61 × 2557</span><br /><span style="color: red;">20. 155981 = 7 × 22283</span><br /><span style="color: red;">21. 155983 = 151 × 1033</span><br /><span style="color: red;">22. 155987 = 13</span> <span style="color: red;">× 13</span> <span style="color: red;">× 13</span> <span style="color: red;">× 71</span><br /><span style="color: red;">23. 155989 = 389 × 401</span><br /><span style="color: red;">24. 155993 = 47 × 3319</span><br /><span style="color: red;">25. 155999 = 257 × 607</span></td>
</tr>
<tr>
<td class="tg-nrix">26</td>
<td class="tg-bxdl"><span style="color: red;">1. 370901 = 421 × 881</span><br /><span style="color: red;">2. 370903 = 13 × 103 × 277</span><br /><span style="color: red;">3. 370907 = 167 × 2221</span><br /><span style="color: red;">4. 370909 = 7 × 11 × 4817</span><br /><span style="color: red;">5. 370913 = 73 × 5081</span><br /><span style="color: black;">370919 is prime</span><br /><span style="color: red;">6. 370921 = 23 × 16127</span><br /><span style="color: red;">7. 370927 = 41 × 83 × 109</span><br /><span style="color: red;">8. 370931 = 11 × 33721</span><br /><span style="color: red;">9. 370933 = 59 × 6287</span><br /><span style="color: red;">10. 370937 = 7 × 19 × 2789</span><br /><span style="color: red;">11. 370939 = 29 × 12791</span><br /><span style="color: red;">12. 370943 = 347 × 1069</span><br /><span style="color: black;">370949 is prime</span><br /><span style="color: red;">13. 370951 = 7 × 197 × 269</span><br /><span style="color: red;">14. 370957 = 17 × 21821</span><br /><span style="color: red;">15. 370961 = 43 × 8627</span><br /><span style="color: red;">16. 370963 = 409 × 907</span><br /><span style="color: red;">17. 370967 = 23 × 127 × 127</span><br /><span style="color: red;">18. 370969 = 107 × 3467</span><br /><span style="color: red;">19. 370973 = 101 × 3673</span><br /><span style="color: red;">20. 370979 = 7</span> <span style="color: red;">× 7</span> <span style="color: red;">× 67 × 113</span><br /><span style="color: red;">21. 370981 = 13 × 28537</span><br /><span style="color: red;">22. 370987 = 349 × 1063</span><br /><span style="color: red;">23. 370991 = 17 × 139 × 157</span><br /><span style="color: red;">24. 370993 = 7 × 52999</span><br /><span style="color: red;">25. 370997 = 11 × 29 × 1163</span><br /><span style="color: red;">26. 370999 = 37</span> <span style="color: red;">× 37</span> <span style="color: red;">× 271</span></td>
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<tr>
<td class="tg-nrix">27</td>
<td class="tg-bxdl"><span style="color: red;">1. 268301 = 11 × 24391</span><br /><span style="color: red;">2. 268303 = 7 × 38329</span><br /><span style="color: red;">3. 268307 = 13 × 20639</span><br /><span style="color: red;">4. 268309 = 71 × 3779</span><br /><span style="color: red;">5. 268313 = 157 × 1709</span><br /><span style="color: red;">6. 268319 = 251 × 1069</span><br /><span style="color: red;">7. 268321 = 179 × 1499</span><br /><span style="color: red;">8. 268327 = 151 × 1777</span><br /><span style="color: red;">9. 268331 = 7 × 38333</span><br /><span style="color: red;">10. 268333 = 13 × 20641</span><br /><span style="color: red;">11. 268337 = 19 × 29 × 487</span><br /><span style="color: red;">12. 268339 = 53 × 61 × 83</span><br /><span style="color: black;">268343 is prime</span><br /><span style="color: red;">13. 268349 = 149 × 1801</span><br /><span style="color: red;">14. 268351 = 127 × 2113</span><br /><span style="color: red;">15. 268357 = 101 × 2657</span><br /><span style="color: red;">16. 268361 = 37 × 7253</span><br /><span style="color: red;">17. 268363 = 43 × 79 × 79</span><br /><span style="color: red;">18. 268367 = 11 × 31 × 787</span><br /><span style="color: red;">19. 268369 = 167 × 1607</span><br /><span style="color: red;">20. 268373 = 7</span> <span style="color: red;">× 7</span> <span style="color: red;">× 5477</span><br /><span style="color: red;">21. 268379 = 17 × 15787</span><br /><span style="color: red;">22. 268381 = 349 × 769</span><br /><span style="color: red;">23. 268387 = 7 × 23 × 1667</span><br /><span style="color: red;">24. 268391 = 59 × 4549</span><br /><span style="color: red;">25. 268393 = 311 × 863</span><br /><span style="color: red;">26. 268397 = 239 × 1123</span><br /><span style="color: red;">27. 268399 = 97 × 2767</span></td>
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<tr>
<td class="tg-nrix">28</td>
<td class="tg-bxdl"><span style="color: red;">1. 6085001 = 13 × 223 × 2099</span><br /><span style="color: red;">2. 6085003 = 139 × 43777</span><br /><span style="color: red;">3. 6085007 = 67 × 90821</span><br /><span style="color: red;">4. 6085009 = 7 × 241 × 3607</span><br /><span style="color: red;">5. 6085013 = 11 × 641 × 863</span><br /><span style="color: red;">6. 6085019 = 89 × 68371</span><br /><span style="color: red;">7. 6085021 = 31 × 196291</span><br /><span style="color: red;">8. 6085027 = 13 × 468079</span><br /><span style="color: red;">9. 6085031 = 17 × 263 × 1361</span><br /><span style="color: red;">10. 6085033 = 313 × 19441</span><br /><span style="color: red;">11. 6085037 = 7 × 869291</span><br /><span style="color: red;">12. 6085039 = 181 × 33619</span><br /><span style="color: red;">13. 6085043 = 47 × 129469</span><br /><span style="color: red;">14. 6085049 = 269 × 22621</span><br /><span style="color: red;">15. 6085051 = 7 × 869293</span><br /><span style="color: red;">16. 6085057 = 11 × 37 × 14951</span><br /><span style="color: red;">17. 6085061 = 73 × 83357</span><br /><span style="color: red;">18. 6085063 = 907 × 6709</span><br /><span style="color: red;">19. 6085067 = 881 × 6907</span><br /><span style="color: red;">20. 6085069 = 191 × 31859</span><br /><span style="color: red;">21. 6085073 = 19 × 320267</span><br /><span style="color: red;">22. 6085079 = 7 × 11 × 13 × 6079</span><br /><span style="color: red;">23. 6085081 = 131 × 46451</span><br /><span style="color: red;">24. 6085087 = 23</span> <span style="color: red;">× 23</span> <span style="color: red;">× 11503</span><br /><span style="color: red;">25. 6085091 = 1013 × 6007</span><br /><span style="color: red;">26. 6085093 = 7 × 869299</span><br /><span style="color: red;">27. 6085097 = 41 × 193 × 769</span><br /><span style="color: red;">28. 6085099 = 17 × 29 × 12343</span></td>
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</table><h4 style="text-align: left;">
Surrounding Centuries Not Shown for Composite Counts Affected by Eight-Digit Gap</h4>
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<th class="tg-7btt">n</th>
<th class="tg-amwm">Factorisations of numbers not divisible by 2, 3, or 5</th>
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<tr>
<td class="tg-nrix">9</td>
<td class="tg-0lax"><span style="color: black;">190818931155803 is prime</span><br /><span style="color: red;">1. 190818931155809 = 11 × 43 × 54851 × 7354883</span><br /><span style="color: red;">2. 190818931155811 = 7 × 7</span> <span style="color: red;">× 3894263901139</span><br /><span style="color: black;">190818931155817 is prime</span><br /><span style="color: black;">190818931155821 is prime</span><br /><span style="color: black;">190818931155823 is prime</span><br /><span style="color: red;">3. 190818931155827 = 13 × 1259 × 11658760381</span><br /><span style="color: red;">4. 190818931155829 = 37 × 983 × 5246458199</span><br /><span style="color: black;">190818931155833 is prime</span><br /><span style="color: red;">5. 190818931155839 = 7 × 17 × 19 × 887 × 95147477</span><br /><span style="color: black;">190818931155841 is prime</span><br /><span style="color: red;">6. 190818931155847 = 59 × 73 × 9883 × 4482887</span><br /><span style="color: black;">190818931155851 is prime</span><br /><span style="color: red;">7. 190818931155853 = 7 × 11 × 13 × 499 × 382020647</span><br /><span style="color: black;">190818931155857 is prime</span><br /><span style="color: black;">190818931155859 is prime</span><br /><span style="color: black;">190818931155863 is prime</span><br /><span style="color: black;">190818931155869 is prime</span><br /><span style="color: black;">190818931155871 is prime</span><br /><span style="color: red;">8. 190818931155877 = 19 × 1571 × 56533 × 113081</span><br /><span style="color: red;">9. 190818931155881 = 7 × 23 × 84509 × 14024669</span><br /><span style="color: black;">190818931155883 is prime</span><br /><span style="color: black;">190818931155887 is prime</span><br /><span style="color: black;">190818931155889 is prime</span><br /><span style="color: black;">190818931155893 is prime</span><br /><span style="color: black;">190818931155899 is prime</span></td>
</tr>
<tr>
<td class="tg-nrix" rowspan="2">10</td>
<td class="tg-0lax"><span style="color: black;">23003 is prime</span><br /><span style="color: red;">1. 23009 = 7 × 19 × 173</span><br /><span style="color: black;">23011 is prime</span><br /><span style="color: black;">23017 is prime</span><br /><span style="color: black;">23021 is prime</span><br /><span style="color: red;">2. 23023 = 7 × 11 × 13 × 23</span><br /><span style="color: black;">23027 is prime</span><br /><span style="color: black;">23029 is prime</span><br /><span style="color: red;">3. 23033 = 31 × 743</span><br /><span style="color: black;">23039 is prime</span><br /><span style="color: black;">23041 is prime</span><br /><span style="color: red;">4. 23047 = 19 × 1213</span><br /><span style="color: red;">5. 23051 = 7 × 37 × 89</span><br /><span style="color: black;">23053 is prime</span><br /><span style="color: black;">23057 is prime</span><br /><span style="color: black;">23059 is prime</span><br /><span style="color: black;">23063 is prime</span><br /><span style="color: red;">6. 23069 = 17 × 23 × 59</span><br /><span style="color: black;">23071 is prime</span><br /><span style="color: red;">7. 23077 = 47 × 491</span><br /><span style="color: black;">23081 is prime</span><br /><span style="color: red;">8. 23083 = 41 × 563</span><br /><span style="color: black;">23087 is prime</span><br /><span style="color: red;">9. 23089 = 11 × 2099</span><br /><span style="color: red;">10. 23093 = 7 × 3299</span><br /><span style="color: black;">23099 is prime</span></td>
</tr>
<tr>
<td class="tg-bxdl"><span style="color: red;">1. 2466269101 = 17 × 61 × 2378273</span><br /><span style="color: black;">2466269107 is prime</span><br /><span style="color: black;">2466269111 is prime</span><br /><span style="color: red;">2. 2466269113 = 7 × 11 × 1201 × 26669</span><br /><span style="color: red;">3. 2466269117 = 13 × 47 × 971 × 4157</span><br /><span style="color: black;">2466269119 is prime</span><br /><span style="color: black;">2466269123 is prime</span><br /><span style="color: red;">4. 2466269129 = 67 × 2269 × 16223</span><br /><span style="color: black;">2466269131 is prime</span><br /><span style="color: black;">2466269137 is prime</span><br /><span style="color: red;">5. 2466269141 = 7 × 19 × 18543377</span><br /><span style="color: red;">6. 2466269143 = 13 × 173 × 541 × 2027</span><br /><span style="color: black;">2466269147 is prime</span><br /><span style="color: black;">2466269149 is prime</span><br /><span style="color: black;">2466269153 is prime</span><br /><span style="color: black;">2466269159 is prime</span><br /><span style="color: black;">2466269161 is prime</span><br /><span style="color: black;">2466269167 is prime</span><br /><span style="color: red;">7. 2466269171 = 43 × 57355097</span><br /><span style="color: black;">2466269173 is prime</span><br /><span style="color: black;">2466269177 is prime</span><br /><span style="color: red;">8. 2466269179 = 11 × 19 × 631 × 18701</span><br /><span style="color: red;">9. 2466269183 = 7 × 103 × 113 × 30271</span><br /><span style="color: black;">2466269189 is prime</span><br /><span style="color: black;">2466269191 is prime</span><br /><span style="color: red;">10. 2466269197 = 7 × 157 × 829 × 2707</span></td>
</tr>
<tr>
<td class="tg-nrix" rowspan="2">11</td>
<td class="tg-bxdl"><span style="color: red;">1. 2967301 = 43 × 151 × 457</span><br /><span style="color: red;">2. 2967307 = 7 × 109 × 3889</span><br /><span style="color: red;">3. 2967311 = 53 × 55987</span><br /><span style="color: red;">4. 2967313 = 719 × 4127</span><br /><span style="color: black;">2967317 is prime</span><br /><span style="color: red;">5. 2967319 = 79 × 37561</span><br /><span style="color: black;">2967323 is prime</span><br /><span style="color: black;">2967329 is prime</span><br /><span style="color: black;">2967331 is prime</span><br /><span style="color: black;">2967337 is prime</span><br /><span style="color: red;">6. 2967341 = 13 × 228257</span><br /><span style="color: black;">2967343 is prime</span><br /><span style="color: black;">2967347 is prime</span><br /><span style="color: red;">7. 2967349 = 7 × 11 × 89 × 433</span><br /><span style="color: black;">2967353 is prime</span><br /><span style="color: black;">2967359 is prime</span><br /><span style="color: black;">2967361 is prime</span><br /><span style="color: red;">8. 2967367 = 13 × 17 × 29 × 463</span><br /><span style="color: red;">9. 2967371 = 11 × 269761</span><br /><span style="color: black;">2967373 is prime</span><br /><span style="color: red;">10. 2967377 = 7 × 73 × 5807</span><br /><span style="color: black;">2967379 is prime</span><br /><span style="color: black;">2967383 is prime</span><br /><span style="color: black;">2967389 is prime</span><br /><span style="color: red;">11. 2967391 = 7 × 7</span> <span style="color: red;">× 23 × 2633</span><br /><span style="color: black;">2967397 is prime</span><br /><span style="color: red;">2967401 = 17 × 19 × 9187</span><br /><span style="color: black;">2967403 is prime</span><br /><span style="color: black;">2967407 is prime</span><br /><span style="color: black;">2967409 is prime</span></td>
</tr>
<tr>
<td class="tg-bxdl"><span style="color: red;">1. 98195303 = 23 × 421 × 10141</span><br /><span style="color: black;">98195309 is prime</span><br /><span style="color: black;">98195311 is prime</span><br /><span style="color: red;">2. 98195317 = 11 × 1621 × 5507</span><br /><span style="color: red;">3. 98195321 = 7 × 31 × 149 × 3037</span><br /><span style="color: black;">98195323 is prime</span><br /><span style="color: black;">98195327 is prime</span><br /><span style="color: black;">98195329 is prime</span><br /><span style="color: black;">98195333 is prime</span><br /><span style="color: red;">4. 98195339 = 11 × 977 × 9137</span><br /><span style="color: red;">5. 98195341 = 79 × 1 242979</span><br /><span style="color: black;">98195347 is prime</span><br /><span style="color: black;">98195351 is prime</span><br /><span style="color: black;">98195353 is prime</span><br /><span style="color: red;">6. 98195357 = 13 × 1511 × 4999</span><br /><span style="color: red;">7. 98195359 = 43 × 103 × 22171</span><br /><span style="color: red;">8. 98195363 = 7 × 7</span> <span style="color: red;">× 19 × 29 × 3637</span><br /><span style="color: red;">9. 98195369 = 41 × 2395009</span><br /><span style="color: black;">98195371 is prime</span><br /><span style="color: red;">10. 98195377 = 7 × 947 × 14813</span><br /><span style="color: black;">98195381 is prime</span><br /><span style="color: red;">11. 98195383 = 11 × 13 × 17 × 31 × 1303</span><br /><span style="color: black;">98195387 is prime</span><br /><span style="color: black;">98195389 is prime</span><br /><span style="color: black;">98195393 is prime</span><br /><span style="color: black;">98195399 is prime</span></td>
</tr>
</tbody>
</table>
In the case of the 29,674<sup>th</sup> century, I have included the first decade of the following century because of the remarkable prime richness of the 100 numbers ending with 2,967,410. The eighteen primes in those 100 numbers is not equalled between 113,180 and 341,078,531,679 (that is, greater than <i>341 billion</i>, or over <i>one hundred thousand times larger in magnitude</i> than the 29,674<sup>th</sup> century), and no consecutive multiples of 100 between 200 and 122,853,771,370,899 contain as many as eighteen primes between them. Moreover, as Brian Kehrig noted in correspondence with me, seven rather than eight is the number of digits for which there should be fewest centuries or sequences exceptionally rich in prime numbers, making the sequence from 2,967,310 to 2,967,410 even more exceptional.<div><br /></div><div>The century from 98,195,300 to 98,195,399 is still within the eight-digit gap — after all, it contains eight digits and not more or less — but the eleven composites not divisible by 2, 3, or 5 is the fewest since the 29,674<sup>th</sup> century and shows one moving away from the “core” of that gap. There are four centuries between 98,195,400 and 839,296,299 containing only eleven composites not divisible by 2, 3, or 5, but it would be superfluous to include all of them and the 981,954<sup>th</sup> century should be reasonably illustrative.</div></div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-44216056342795234032023-08-28T21:53:00.236+10:002023-12-19T00:28:08.824+11:00An alternative view of primes in centuries<p>The OEIS sequences at <a href="https://oeis.org/A038822">A038822</a> and <a href="https://oeis.org/A186311">A186311</a> have long been familiar to me ever since I first studied primes as a high school student reading the old <b><u>Mathematics Around Us: Skills and Applications</u></b> book from my primary school years. As a teenager, I would attempt to factor numbers beyond the prime table my late uncle gave me and memorises the primes up to 2,000 — something which I like to practice with my mobile on buses and even to quiz others with no interest in primes about.</p><p>When I studied primes in the second millennium, I notices very early on that there was a discrepancy between centuries in the number of possible primes, although at the time I naturally could not recognise the exact extent of the actual limits found in sequence A186311. I noticed that</p><p></p><ul style="text-align: left;"><li>every third century had <i>28 numbers not divisible by 2, 3, or 5</i> —</li><ul><li>I knew elementary divisibility tests for the prime numbers 2, 3, and 5 as a child, so I knew immediately numbers which passed those tests could not be prime</li></ul><li>the other two centuries in each set of 3 had only <i>26 numbers not divisible by 2, 3, or 5</i></li><li>that centuries with 28 numbers not divisible by 2, 3, or 5 began with a number of the form 300<b>k</b>+100</li><li>that centuries with 26 numbers not divisible by 2, 3, or 5 began with a number of the form 300<b>k</b> or 300<b>k</b>+200</li></ul><div>As I memorised primes, I also memorised the factors of composite numbers not divisible by 2, 3, or 5 — all of them up to 2,000 and sporadically up to 10,000 and even beyond in some special cases. Although I was not aware of it until recently, I early on noticed clusters with unusually many or few numbers whose factorisations required memorisation — in layman’s terms, <i>composite numbers not divisible by 2, 3, or 5</i>.</div><div><br /></div><div>It is only recently, when I have come to study prime-rich centuries beyond the “eight-digit gap” (in layman’s terms, numbers greater than 839,296,300) that I have attempted to actually sequence the number of composite numbers not divisible by 2, 3 or 5 in each century. The sequence of number of composite numbers not divisible by 2, 3, or 5 between 100<b>k</b> and 100<b>k</b>+99 begins thus:</div><div><br /></div><div>3, 7, 10, 10, 11, 12, 10, 14, 11, 12, 12, 14, 11, 17, 9, 14, 13, 14, 14, 15, 12, 16, 13, 11, 16, 17, 11, 12, 16, 15, 14, 18, 15, 11, 17, 12, 13, 16, 15, 15, 13, 17, 10, 19, 15, 14, 16, 14, 18, 13, 14, 15, 18, 16, 13, 15, 14, 16, 12, 19, 14, 17, 13, 11, 20, 15, 16, 16, 14, 13, 19, 16, 15, 19, 15, 11, 16, 16, 16, 18, 15, 16, 14, 17, 18, 16, 13, 15, 15, 17, 15, 16, 15, 15, 13, 19, 13, 17, 14, 17, 17, 14, 16, 16, 16, 18, 16, 15, 16, 18, 16, 15, 18, 16, 15, 19, 18, 17, 16, 13, 17, 17, 14, 17, 15, 14, 14, 18, 17, 14, 17, 14, 17, 18, 15, 18, 16, 14, 17, 17, 16, 18, 21, 17, 14, 16, 16, 12, 16, 18, 17, 16, 14, 14, 17, 18, 13, 16, 17, 16, 16, 17, 18, 19, 14, 19, 15, 19, 17, 16, 15, 17, 19, 14, 13, 18, 18, 16, 20, 12, 16, 17, 15, 15, 17, 16, 20, 17, 21, 18, 17, 19, 15, 19, 10, 15, 21, 16, 16, 16, 17, 13, 19, 14, 18, 18, 19, 14, 19, 17, 15, 15, 19, 15, 18, 13, 17, 17, 15, 18, 15, 14, 17, 19, 18, 17, 16, 15, 18, 19, 10, 18, 18, 17, 20, 16, 14, 17, 15, 17, 13, 16, 19, 18, 18, 18, 17, 20, 18, 15, 20, 15, 19, 16, 16, 18, 16, 16, 18, 16, 18, 15, 17, 16, 16, 20, 16, 15, 16, 16, 16, 20, 16, 21, 18, 18, 17, 14, 17, 15, 17, 19, 17, 21, 15, 14, 14, 16, 17, 20, 17, 15, 18, 15, 17, 18, 18, 19, 18, 19, 17, 16, 17, 17, 19, 17, 17, 20, 13, 18, 18, 14, 15, 16, 22, 16, 18, 16, 19, 22, 13, 17, 19, 13, 15, 17, 17, 16, 20, 13, 16, 18, 20, 14, 18, 14, 16, 16, 16, 18, 22, 17, 15, 17, 16, 16, 17, 17, 16, 21, 16, 17, 19, 17, 17, 15, 22, 19, 16, 16, 16, 20, 16, 17, 19, 15, 16, 16, 17, 15, 18, 18, 19, 16, 18, 11, 18, 21, 16, 19, 20, 17, 18, 16, 20, 21, 14, 15, 19, 16, 18, 16, 17, 14, 21, 17, 18, 17, 14, 18, 19, 15, 18, 23, 16, 16, 21, 19, 13, 20, 17, 15, 15, 18, 19, 18, 13, 19, 17, 14, 16, 18, 16, 16, 13, 19, 17, 15, 18, 16, 19, 19, 18, 21, 17, 18, 18, 15, 21, 17, 16, 16, 15, 20, 20, 17, 15, 16, 19, 16, 20, 17, 19, 16, 20, 16, 17, 21, 15, 19, 19, 16, 19, 19, 16, 17, 17, 18, 15, 22, 19, 16, 19, 16, 18, 16, 17, 15, 20, 15, 19, 18, 19, 18, 16, 17, 17, 18, 15, 20, 18, 14, 17, 19, 15, 18, 18, 17, 16, 18, 16, 16, 19, 16, 19, 16, 21, 18, 19, 17, 19, 18, 17, 18, 14, 15, 16, 20, 15, 17, 20, 16, 17, 19, 22, 14, 20, 17, 17, 17, 17, 15, 19, 19, 18, 19, 14, 18, 17, 18, 18, 19, 20, 17, 15, 15, 17, 18, 20, 17, 19, 19, 16, 18, 20, 19, 14, 18, 14, 18, 17, 17, 19, 19, 15, 16, 18, 16, 17, 13, 18, 17, 16, 16, 22, 18, 17, 16, 17, 18, 18, 15, 18, 18, 16, 19, 18, 17, 23, 16, 14, 16, 18, 16, 15, 21, 14, 16, 23, 19, 17, 18, 17, 18, 21, 21, 13, 17, 19, 17, 19, 20, 18, 20, 16, 17, 15, 19, 19, 18, 16, 17, 20, 19, 17, 19, 17, 18, 20, 15, 19, 20, 20, 13, 17, 17, 13, 17, 18, 19, 19, 18, 19, 20, 18, 20, 17, 19, 18, 20, 16, 14, 20, 18, 17, 16, 16, 16, 18, 17, 18, 19, 22, 17, 19, 16, 19, 18, 17, 17, 19, 15, 16, 21, 13, 16, 21, 15, 17, 16, 19, 20, 19, 20, 17, 19, 18, 16, 19, 19, 18, 18, 18, 18, 14, 23, 20, 21, 16, 19, 18, 14, 16, 19, 17, 17, 19, 19, 17, 14, 19, 17, 19, 13, 15, 19, 20, 18, 16, 15, 17, 20, 15, 18, 20, 20, 15, 19, 18, 14, 18, 20, 21, 18, 18, 16, 17, 19, 17, 21, 17, 16, 18, 17, 18, 17, 20, 14, 17, 20, 18, 20, 16, 16, 22, 14, 16, 16, 21, 16, 20, 19, 16, 21, 17, 17, 19, 19, 17, 20, 17, 19, 16, 17, 17, 15, 16, 15, 20, 19, 19, 17, 19, 19, 20, 15, 19, 19, 16, 19, 23, 15, 18, 16, 19, 19, 14, 23, 13, 17, 21, 16, 17, 18, 18, 22, 13, 16, 20, 17, 12, 19, 18, 18, 22, 16, 16, 18, 19, 16, 17, 17, 16, 19, 17, 17, 20, 15, 19, 22, 16, 22, 15, 19, 14, 21, 18, 18, 21, 18, 18, 18, 18, 17, 16, 18, 18, 19, 19, 18, 18, 18, 17, 20, 17, 18, 17, 19, 17, 22, 19, 15, 16, 15, 18, 18, 21, 18, 21, 17, 19, 18, 16, 20, 19, 13, 14, 19, 18, 17, 20, 22, 19, 21, 18, 21, 19, 18, 13, 21, 15, 18, 18, 17, 18, 16, 15, 20, 18, 17, 13, 18, 17, 19, 19, 18, 17, 22, 18, 16, 21, 14, 18, 18, 17, 18, 23, 19, 17, 18, 19, 17, 18, 13, 17, 20, 14, 16, 17, 18, 18, 18, 16, 18, 18, 18, 21, 21, 18, 14, 20, 19, 18, 17, 17, 15, 21, 17, 17, 20, 16, 17, 16, 19, 15, 19, 20, 14, 19, 16, 18, 21, 16, 20, 16, 19, 20, 16, 19, 17, 21, 16, 21, 18, 19, 15, 21, 20, 15, 20, 19, 21, 19, 17, 15, 20, 19, 18, 16, 15, 18, 17, 18, 18, 21, 17, 18, 18, 16, 18, 22, 17, 18, 19, 18, 16, 20, 19, ...</div><div><br /></div><div>Put as a table, the first 100 centuries are:</div><style type="text/css">
.tg {border-collapse:collapse;border-spacing:2;}
.tg td{border-color:black;border-style:solid;border-width:2px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:5px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:2px;font-family:Arial, sans-serif;font-size:14px;
font-weight:normal;overflow:hidden;padding:5px 5px;word-break:normal;}
.tg .tg-cly1{text-align:left;vertical-align:middle}
.tg .tg-yla0{font-weight:bold;text-align:left;vertical-align:middle}
</style>
<table class="tg">
<thead>
<tr>
<th class="tg-yla0"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">k</span></th>
<th class="tg-yla0">n</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">21</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">22</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">24</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">25</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">26</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">28</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">29</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">30</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">31</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">32</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">33</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">34</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">35</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">36</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">37</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">38</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">39</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">40</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">41</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">42</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">43</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">44</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">45</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">46</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">47</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">48</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">49</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">50</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">51</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">52</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">53</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">54</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">55</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">56</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">57</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">58</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">59</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">60</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">61</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">62</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">63</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">64</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">65</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">66</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">67</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">68</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">69</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">70</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">71</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">72</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">73</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">74</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">75</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">76</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">77</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">78</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">79</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">80</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">81</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">82</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">83</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">84</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">85</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">86</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">87</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">88</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">89</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">90</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">91</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">92</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">93</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">94</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">95</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">96</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">97</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">98</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">99</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
</tr>
</tbody>
</table>
One can also consider the smallest centuries with <i>n</i> composites not divisible by 2, 3, or 5, which I will tabulate below:
<style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:2px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:2px;
font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;}
.tg .tg-cly1{text-align:left;vertical-align:middle}
.tg .tg-lboi{border-color:inherit;text-align:left;vertical-align:middle}
.tg .tg-nrix{text-align:center;vertical-align:middle}
.tg .tg-uzvj{border-color:inherit;font-weight:bold;text-align:center;vertical-align:middle}
.tg .tg-za14{border-color:inherit;text-align:left;vertical-align:bottom}
</style>
<table class="tg" style="table-layout: fixed; width: 933px;">
<colgroup>
<col style="width: 43px;"></col>
<col style="width: 890px;"></col>
</colgroup>
<thead>
<tr>
<th class="tg-nrix"><span style="font-style: italic; font-weight: normal;">n</span></th>
<th class="tg-uzvj"><span style="font-weight: normal;">smallest </span><span style="font-weight: bold;">k</span><span style="font-weight: normal;">s</span></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-nrix">0</td>
<td class="tg-lboi">(not possible)</td>
</tr>
<tr>
<td class="tg-nrix">1</td>
<td class="tg-lboi">(not possible)</td>
</tr>
<tr>
<td class="tg-nrix">2</td>
<td class="tg-lboi">(not possible)</td>
</tr>
<tr>
<td class="tg-nrix">3</td>
<td class="tg-lboi">0, ...</td>
</tr>
<tr>
<td class="tg-nrix">4</td>
<td class="tg-lboi">(unknown)</td>
</tr>
<tr>
<td class="tg-nrix">5</td>
<td class="tg-lboi">(unknown)</td>
</tr>
<tr>
<td class="tg-nrix">6</td>
<td class="tg-cly1">..., 394338677302163715754576644, 6228039143760643018587824345, ...</td>
</tr>
<tr>
<td class="tg-nrix">7</td>
<td class="tg-lboi">1, ...</td>
</tr>
<tr>
<td class="tg-nrix">8</td>
<td class="tg-lboi">23352869714018, 983930290209021, ...</td>
</tr>
<tr>
<td class="tg-nrix">9</td>
<td class="tg-lboi">14, 1908189311558, 6157376214122, 7658205745776, 8078877131667, 10137710652198, 13862924841999, 17176990713081, 18883149995801, 19441702516473, 22930638581651, 27366580054772, 28441016502165, 34640826787757, 45813173440655, 56510624356859, ..., 14688670051164208, ...</td>
</tr>
<tr>
<td class="tg-nrix">10</td>
<td class="tg-lboi">2, 3, 6, 42, 194, 230, 24662691, 313114319, 776749247, 2013136112, 6569717174, 16226936180, 20473355126, 23861161886, 27524565569, 28137314864, 30609996072, 30703228932, 30730057202, 30938308631, 32111780141, 44049425619, 59164187718, 59297737052, 69898357008, ..., 1228537713709, ...</td>
</tr>
<tr>
<td class="tg-nrix">11</td>
<td class="tg-lboi">4, 8, 12, 23, 26, 33, 63, 75, 375, 1131, 1572, 7837, 9780, 17492, 27049, 29673, 981953, 1040840, 3145701, 6936645, 6970379, 8560196, 9016406, 9255944, 9520169, 15112118, 17187179, 27261180, 39759303, 58470222, 60393431, 69026496, 93078120, 96687828, 99524981, 101914209, 105652944, 115354109, 121978380, 124847702, 129567821, 144997771, 155326974, 170092302, ...</td>
</tr>
<tr>
<td class="tg-nrix">12</td>
<td class="tg-lboi">5, 9, 10, 20, 27, 35, 58, 147, 179, 810, 1158, 1416, 2033, 2232, 2297, 2660, 3054, 4508, 6635, 8237, 12303, 12463, 16166, 21728, 26640, 28029, 58514, 82325, 138302, 143576, 155249, 182004, 206582, 236156, 280235, 290367, 301551, 490343, 498444, 654080, 800232, 914537, 973409, 1080495, 1134048, 1199364, 1238217, 1256649, 1257629, 1311918, 1396323, 1599869, 1689077, 1927515, 1978332, ...</td>
</tr>
<tr>
<td class="tg-nrix">13</td>
<td class="tg-lboi">16, 22, 36, 40, 49, 54, 62, 69, 86, 94, 96, 119, 156, 174, 201, 215, 240, 308, 320, 323, 329, 408, 416, 424, 569, 606, 633, 636, 674, 713, 798, 806, 875, 888, 900, 923, 1098, 1122, 1130, 1247, 1317, 1670, 1799, 1833, 1871, 2303, 2676, 2847, 2891, 3122, 3177, 3213, 3442, 3543, 3922, 4065, 4203, 4676, 4784, 5249, 5415, 5595, 6441, 7393, 7488, 7883, 8021, 8412, 8444, 8603, 9290, 9843, 9903, ...</td>
</tr>
<tr>
<td class="tg-nrix">14</td>
<td class="tg-lboi">7, 11, 15, 17, 18, 30, 45, 47, 50, 56, 60, 68, 82, 98, 101, 122, 125, 126, 129, 131, 137, 144, 152, 153, 164, 173, 203, 207, 221, 236, 277, 285, 286, 311, 333, 335, 386, 393, 398, 419, 491, 514, 525, 536, 556, 558, 590, 596, 651, 694, 701, 709, 729, 747, 755, 796, 834, 876, 911, 926, 939, 957, 1011, 1047, 1053, 1089, 1109, 1146, 1157, 1169, 1196, 1208, 1220, 1260, 1272, 1289, 1326, 1363, 1373, 1406, 1460, 1763, 1817, 2043, 2054, 2075, 2173, 2199, 2507, 2586, 2621, 2669, 2723, 2748, 2759, 2864, ...</td>
</tr>
<tr>
<td class="tg-nrix">15</td>
<td class="tg-lboi">19, 29, 32, 38, 39, 44, 51, 55, 65, 72, 74, 80, 87, 88, 90, 92, 93, 107, 111, 114, 124, 134, 166, 170, 182, 183, 192, 195, 210, 211, 213, 218, 220, 227, 238, 249, 251, 261, 267, 279, 284, 291, 293, 312, 324, 342, 355, 365, 369, 387, 401, 411, 412, 427, 437, 442, 446, 458, 468, 477, 479, 488, 494, 515, 518, 531, 544, 545, 564, 581, 594, 616, 629, 671, 677, 714, 719, 722, 726, 775, 777, 785, 791, 827, 832, 861, 863, 890, 896, 945, 954, 975, 978, 984, 989, 1020, 1062, 1067, 1082, 1091, 1095, ...</td>
</tr>
<tr>
<td class="tg-nrix">16</td>
<td class="tg-lboi">21, 24, 28, 37, 46, 53, 57, 66, 67, 71, 76, 77, 78, 81, 85, 91, 102, 103, 104, 106, 108, 110, 113, 118, 136, 140, 145, 146, 148, 151, 157, 159, 160, 169, 177, 180, 185, 197, 198, 199, 226, 235, 241, 253, 254, 256, 257, 259, 263, 264, 266, 268, 269, 270, 272, 287, 301, 313, 315, 317, 327, 330, 336, 337, 338, 344, 345, 348, 350, 358, 359, 360, 362, 366, 367, 373, 378, 383, 389, 391, 404, 405, 420, 422, 423, 429, 440, 441, 447, 449, 453, 455, 461, 464, 471, 473, 475, 484, 498, ...</td>
</tr>
<tr>
<td class="tg-nrix">17</td>
<td class="tg-lboi">13, 25, 34, 41, 61, 83, 89, 97, 99, 100, 117, 120, 121, 123, 128, 130, 132, 138, 139, 143, 150, 154, 158, 161, 168, 171, 181, 184, 187, 190, 200, 209, 216, 217, 222, 225, 233, 237, 239, 246, 262, 276, 278, 280, 282, 288, 290, 294, 300, 302, 303, 305, 306, 321, 325, 326, 341, 343, 346, 347, 351, 353, 354, 363, 368, 381, 392, 395, 397, 410, 418, 426, 434, 439, 445, 451, 456, 465, 466, 476, 485, 486, 492, 497, 509, 512, 519, 522, 527, 528, 529, 530, 538, 543, 546, 549, 560, 561, 568, 571, 576, 578, 587, ...</td>
</tr>
<tr>
<td class="tg-nrix">18</td>
<td class="tg-lboi">31, 48, 52, 79, 84, 105, 109, 112, 116, 127, 133, 135, 141, 149, 155, 162, 175, 176, 189, 204, 205, 214, 219, 224, 228, 231, 232, 243, 244, 245, 248, 255, 258, 260, 274, 275, 292, 295, 296, 298, 309, 310, 316, 331, 334, 339, 370, 371, 374, 376, 382, 390, 396, 399, 402, 413, 415, 421, 428, 432, 435, 436, 467, 474, 481, 483, 487, 490, 495, 496, 499, 507, 511, 513, 534, 537, 539, 540, 547, 553, 557, 559, 566, 570, 575, 579, 580, 582, 583, 586, 592, 601, 603, 612, 619, 627, 638, 641, 644, 648, 653, 658, 660, 667, ...</td>
</tr>
<tr>
<td class="tg-nrix">19</td>
<td class="tg-lboi">43, 59, 70, 73, 95, 115, 163, 165, 167, 172, 191, 193, 202, 206, 208, 212, 223, 229, 242, 252, 281, 297, 299, 304, 318, 322, 352, 357, 364, 372, 379, 388, 400, 407, 414, 417, 425, 430, 431, 448, 452, 459, 460, 462, 463, 470, 472, 480, 482, 493, 502, 504, 508, 510, 523, 532, 533, 535, 541, 550, 551, 555, 562, 563, 585, 599, 608, 610, 617, 618, 623, 625, 630, 639, 640, 642, 647, 661, 664, 666, 670, 680, 682, 685, 688, 689, 699, 703, 706, 707, 710, 712, 715, 727, 737, 761, 766, 767, 771, 779, 780, 782, 783, 786, 787, 789, 794, 795, ...</td>
</tr>
<tr>
<td class="tg-nrix">20</td>
<td class="tg-lboi">64, 178, 186, 234, 247, 250, 265, 271, 289, 307, 328, 332, 361, 380, 384, 409, 443, 444, 450, 454, 478, 489, 517, 520, 526, 542, 548, 554, 611, 613, 622, 628, 631, 632, 643, 645, 649, 652, 681, 683, 696, 716, 721, 724, 725, 731, 746, 749, 751, 760, 769, 778, 784, 808, 826, 853, 873, 880, 897, 925, 940, 949, 956, 963, 966, 977, 979, 985, 1006, 1008, 1042, 1044, 1050, 1058, 1065, 1072, 1083, 1097, 1110, 1126, 1127, 1134, 1141, 1143, 1144, 1145, 1149, 1154, 1159, 1160, 1162, 1165, 1166, 1180, 1181, 1185, 1189, 1201, 1212, 1217, 1221, ...</td>
</tr>
<tr>
<td class="tg-nrix">21</td>
<td class="tg-za14">142, 188, 196, 273, 283, 349, 377, 385, 394, 406, 433, 438, 457, 506, 595, 604, 605, 673, 676, 697, 732, 739, 758, 763, 800, 835, 838, 866, 868, 883, 885, 889, 910, 936, 937, 946, 961, 970, 972, 976, 981, 994, 1031, 1032, 1054, 1057, 1074, 1086, 1090, 1096, 1099, 1103, 1120, 1128, 1135, 1136, 1168, 1174, 1193, 1194, 1218, 1248, 1255, 1258, 1261, 1265, 1273, 1279, 1280, 1287, 1293, 1298, 1315, 1318, 1372, 1378, 1387, 1396, 1400, 1441, 1446, 1453, 1471, 1479, 1480, 1496, 1519, ...</td>
</tr>
<tr>
<td class="tg-nrix">22</td>
<td class="tg-za14">314, 319, 340, 356, 469, 524, 574, 662, 754, 805, 814, 829, 831, 859, 881, 907, 1000, 1027, 1037, 1051, 1101, 1124, 1132, 1138, 1183, 1231, 1270, 1307, 1309, 1370, 1423, 1433, 1501, 1531, 1549, 1588, 1623, 1630, 1672, 1681, 1713, 1733, 1755, 1808, 1813, 1837, 1843, 1852, 1864, 1880, 1882, 1900, 1909, 1924, 1956, 1963, 1990, 2031, 2035, 2134, 2149, 2150, 2152, 2164, 2178, 2182, 2191, 2200, 2202, 2222, 2224, 2231, 2330, 2335, 2353, 2404, 2425, ...</td>
</tr>
<tr>
<td class="tg-nrix">23</td>
<td class="tg-za14">403, 588, 598, 695, 790, 797, 916, 1060, 1075, 1204, 1240, 1390, 1430, 1651, 1675, 1751, 1809, 1869, 1885, 1904, 1913, 1942, 1987, 2042, 2067, 2123, 2127, 2278, 2290, 2311, 2317, 2322, 2338, 2449, 2464, 2471, 2505, 2530, 2562, 2590, 2644, 2698, 2743, 2758, 2773, 2779, 2862, 2869, 2874, 2887, ...</td>
</tr>
<tr>
<td class="tg-nrix">24</td>
<td class="tg-za14">1801, 1831, 2374, 2503, 2545, 2611, 2656, 2659, 2665, 2956, 2989, 3020, 3079, 3262, 3394, 3445, 3481, 3574, 3598, 3607, 3658, 3811, 4024, 4051, 4381, 4390, 4453, 4484, 4597, 4617, 4630, 4806, 4819, 4849, 4852, 5023, 5072, 5317, 5374, 5386, 5404, 5423, 5434, 5533, 5551, 5614, 5616, 5632, 5890, ...</td>
</tr>
<tr>
<td class="tg-nrix">25</td>
<td class="tg-za14">1559, 1621, 2734, 2833, 2935, 3679, 3703, 4133, 4276, 4534, 4582, 4771, 5314, 5347, 5443, 5464, 5956, 6100, 7087, 7090, 7177, 7495, 7546, 7621, 7930, 8056, 8224, 8293, 8455, 8995, 9103, 9136, 9667, 9739, 10114, 10279, 10339, 10402, 10606, 10759, 10828, 11194, 11400, 11461, 11524, 11539, 11656, 11773, ...</td>
</tr>
<tr>
<td class="tg-nrix">26</td>
<td class="tg-za14">3709, 4921, 8728, 9796, 10720, 10852, 11953, 11992, 12907, 13495, 13885, 14401, 14497, 14968, 15304, 15427, 15997, 16132, 16564, 16718, 18361, 19513, 20308, 20848, 21235, 22543, 22807, 22903, 22945, 24037, 24844, 26134, 26197, 26378, 26404, 26824, 27025, 28405, 28408, 28462, 28522, 28567, 29455, 29533, 29575, 29788, 30478, 30571, ...</td>
</tr>
<tr>
<td class="tg-nrix">27</td>
<td class="tg-za14">2683, 10048, 12727, 14443, 14680, 15619, 20452, 26257, 30232, 31072, 33439, 34345, 35455, 38086, 38794, 40441, 41194, 44119, 46627, 47305, 52111, 53986, 54121, 54430, 64495, 67015, 68083, 68797, 69721, 70060, 71260, 71602, 72418, 73051, 76213, 77026, 77713, 79462, 80014, 81118, 81661, 82492, 85477, 88069, 89695, 91015, 94348, 94678, 96898, 97324, 99679, ...</td>
</tr>
<tr>
<td class="tg-nrix">28</td>
<td class="tg-za14">60850, 71299, 75652, 83674, 101527, 103438, 105916, 111772, 115558, 115816, 131194, 140872, 146713, 156418, 176101, 179332, 231769, 249472, 264763, 266338, 267481, 291379, 298348, 310513, 319273, 323791, 327508, 363397, 363562, 380893, 387175, 387799, 402937, 404548, 407878, 409723, 418159, 434083, 434356, 436135, ...</td>
</tr>
</tbody>
</table>No century for n = 4 or n = 5 is yet known, and none beyond the second century for n = 7. Dickson’s conjecture from 1904 does imply centuries with 4 or 5 composite numbers not divisible by 2, 3, or 5 exist, although none have yet been discovered.<div><br /><div>If a century has the maximum 23 primes, there are 14 possible patterns with 5 composite numbers not divisible by 2, 3, or 5, and 6 with 3. I have not seen the figures for 22-prime centuries, but the six 23-prime patterns with 3 composite numbers not divisible by 2, 3, or 5 must allow for a century with 4 such numbers by deletion of one prime.</div></div><div><br /></div><div>As a last note for this post, I will tabulate the number of centuries with <b><i>n</i></b> composites not divisible by 2, 3, or 5 for each hundred thousand in the first million:</div>
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<table class="tg" style="table-layout: fixed; width: 910px;">
<colgroup>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 85px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
<col style="width: 75px;"></col>
</colgroup>
<thead>
<tr>
<th class="tg-amwm" colspan="12">Number of Centuries Containing <span style="font-style: italic;">n</span> Composite Numbers Not Divisible by 2, 3, or 5 in Each Hundred Thousand of the First Million</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-wa1i"><span style="color: black; font-style: italic; text-decoration: none;"><b>n</b></span></td>
<td class="tg-wa1i"><b><span style="color: black; font-style: normal; text-decoration: none;">Total #</span><br /><span style="color: black; font-style: normal; text-decoration: none;">in First Million</span></b></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>First</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Second</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Third</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Fourth</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Fifth</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Sixth</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Seventh</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Eighth</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Ninth</b></span></td>
<td class="tg-wa1i"><span style="color: black; font-style: normal; text-decoration: none;"><b>Tenth</b></span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">73</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">36</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">178</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">62</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">21</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">409</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">95</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">58</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">32</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">34</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">46</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">33</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">34</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">791</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">165</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">104</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">101</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">76</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">57</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">78</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">54</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">54</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">50</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">52</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">17</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1,195</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">172</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">160</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">131</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">130</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">109</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">109</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">111</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">84</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">106</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">83</span></td>
</tr>
<tr>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">18</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1,658</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">173</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">195</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">197</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">174</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">160</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">165</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">143</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">157</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">152</span></td>
<td class="tg-cly1"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">142</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">19</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1,796</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">136</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">160</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">183</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">184</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">172</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">187</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">210</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">189</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">171</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">204</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1,601</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">68</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">141</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">156</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">169</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">193</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">172</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">160</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">192</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">173</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">177</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">21</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1,160</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">42</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">87</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">93</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">104</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">132</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">132</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">133</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">137</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">150</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">150</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">22</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">621</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">41</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">45</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">59</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">62</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">65</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">73</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">82</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">88</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">90</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">23</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">318</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">16</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">28</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">29</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">26</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">37</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">48</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">35</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">48</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">44</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">24</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">119</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">21</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">20</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">25</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">34</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">26</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">27</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">28</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
</tbody>
</table>The pattern we see here, although much more limited than <a href="https://archive.org/details/factortablefors00glaigoog/page/n62/mode/2up">the study of primes in centuries by James Glaisher from the late 1870s</a>, is very similar to Glaisher’s findings:
<div><ol style="text-align: left;"><li>in the first hundred thousand centuries with <i>seventeen</i> and <i>eighteen</i> composites not divisible by 2, 3, or 5 are virtually equally the most numerous</li><li>in the second and third hundred thousand centuries with <i>eighteen</i> composites not divisible by 2, 3, or 5 are clearly the most numerous</li><li>in the remaining hundred thousands centuries with <i>nineteen</i> composites not divisible by 2, 3, or 5 are the most numerous.</li><ul><li>however, in the eighth and ninth hundred thousand centuries with twenty composites not divisible by 2, 3, or 5 are virtually equal in number to those with nineteen</li></ul><li>in the whole first million centuries with nineteen composites not divisible by 2, 3, or 5 are most numerous, followed by those with eighteen and twenty such numbers (almost equal) and those with seventeen and twenty-one composites not divisible by 2, 3, or 5 (also almost equal).</li></ol><div>Glaisher found that in the first million centuries with <i>eight primes</i> were most numerous. These may contain either eighteen or twenty composites not divisible by 2, 3, or 5. A century with nineteen composites not divisible by 2, 3, or 5 may have either seven or nine primes — the total number of seven- and nine-prime centuries in the first million is indeed greater than the total number of any other pair of prime counts separated by two. If we follow from Glaisher’s table, we would predict — though it would be extremely laborious to check with the tools I possess — that centuries with 21 composites not divisible by 2, 3, or 5 would become the most numerous from the sixth million, and centuries with 20 from the third to the fifth or sixth.</div></div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-40693129957409296142023-08-04T17:32:00.128+10:002023-08-07T20:57:31.332+10:00Another sign of the runaway — Melbourne’s first rainless August<p>Today was a rather difficult sleep for me due to the strong winds overnight. I was later to bed than I had been over the previous few days when I have been affected by a headache and went to bed extremely early a few nights ago.</p><p>Given that there is no rain in the forecast apart from today, I was eagerly awaiting rain from the moment I first briefly woke up around 7 o‘clock to go to the toilet — before getting a very interrupted sleep. I was looking for signs of rain all the time this morning and afternoon, trying half-heartedly to not discuss or look at the weather to see if it was going to rain. BOM forecasts are very unfavourable for significant rain but not so extreme as I was already anticipating from reading them about a week ago, when Melbourne was in danger of its driest July on record.</p><p>All along until around 4 P.M. I was anticipating rain, but when I finally bit the bullet and had a look at BOM’s forecast I found what I feared all along — that Melbourne was not going to get rainfall predicted with a <i>ninety percent</i> chance in the early morning forecast. There is no confident rain in the weekly forecast either, and I have no desire checking further ahead as the seasonal outlook is for very dry and hot weather.</p><h2 style="text-align: left;">Probable Weather for Remainder of 2023:</h2><ol style="text-align: left;"><li>Melbourne will have its first ever rainless August</li><ul><li>the previous record dry August is 12.4 millimetres in 1903</li><li>in fact there has <i>never</i> previously been an August with no rain in the first <i>eight</i> days, but none is forecasted from Saturday until well after that</li></ul><li>Melbourne will not get any rainfall in September or October either, or maximally a small fraction of the sum of the monthly record lows of 19.4 millimetres</li><li>Melbourne’s dry spell record of forty days — ironically set following a record wet spell of 374 millimetres in 42 days and during the city’s wettest ever twelve months with 1,045.5 millimetres between October 1954 and September 1955 — will be beaten by a large margin during the normally rainy winter months</li><ul><li>if Melbourne beats it by the margin Sydney did in 1995 — 47 days vis-à-vis a previous record of 34 — Melbourne would go without rain for at least <i>55 days</i> from 1 August until <i>24 September</i></li><li>Even during the extreme droughts of 1914, 1982 and 2006, there was no rainless spell longer than <i>28 days</i></li></ul><li>Melbourne’s annual rainfall will be below 332 millimetres virtually every year from 2024, and below 166 millimetres most years</li><li>Melbourne’s dams will be permanently dry soon after 2024, with the last runoff-producing rain having occurred this June</li></ol>It has long occurred to me that runaway poleward movement of the frontal systems to well south of Tasmania is long overdue based on circulation changes observed since 1964. These changes would, <a href="http://jpbenney.blogspot.com/2019/03/the-lag-between-tropical-expansion-and.html">as I noted four-and-a-half years ago</a>, mean that Melbourne receives no more than <i>180 millimetres</i> of rainfall per year — and possibly given topographic effects much less than that. With more frequent positive Indian Ocean Dipoles, that figure should decline still further to <i>under 100 millimetres per year</i>.<div><br /></div><div>Such a rapid “catch-up decline” would put an end to most of the attractive feature of Melbourne that the Public Transport Users’ Association noted as already threatened a quarter of a century ago. It shows that runaway climate change was already a danger then. Moreover, the PTUA’s proposals were in fact <i>not nearly radical enough</i>. What was needed was <i>100 percent reduction in car use and a 100 percent reduction in Australia emissions no later than 2005</i>. This was and is — via rational planning and expropriation of the rich polluters — achievable without mobility loss and indeed with mobility gain by eliminating congestion. In addition, even if this rational planning cannot does not reverse runaway climate change and the transformation of Melbourne into a hyperarid desert, it will mean that the polluters responsible are made to pay the cost.</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-78676854308756076202023-07-18T13:56:00.050+10:002023-08-04T20:32:03.971+10:00The thing that must never be said – it overlooks the issue<p>Today, Mummy and I went on a train ride to pick up the new Peugeot, which had a major fault in its brake control that had to be repaired at a workshop near the bend of Hawthorn Road into Camberwell Road. In earlier years, this area was familiar, but since COVID we have never been there.</p><p>On the whole, I enjoyed the return trip with my mother to pick up the car — a 2018 Peugeot 208 which was bought in Balwyn last summer. I was really very reactive to any complaint about the standard of Melbourne’s public transport, which by global standards is exceedingly bad. There remains the problem of loud, one-way “mantras” about the need to end all spending on roads and to transfer it to public transport. Nevertheless, so early as 1990, <b><u>Environment, Capitalism and Socialism</u></b> demonstrated the potential benefits to the immense majority of such a policy, while much more recently <a href="https://www.ecologicalcitizen.net/pdfs/Vol%203%20Suppl%20B.pdf">Richard Smith</a> had demonstrated the urgent necessity of radically reducing car production and banning the manufacture of all but the smallest road vehicles.</p><p>Given what Smith reveals about the energy costs of car production, one must <i>never</i> say that cars are a necessary benefit when criticising Australia’s woeful public transport. Cars’ environmental cost is far too great to, even given the standard of public transport in Australia, excuse their use.</p><p>The fact is — as known for over three decades — that a rational plan could with <i>100 percent public transport modal share</i> and resultant vastly reduced greenhouse emissions and pollution nevertheless produce the same (or greater) mobility cars provide, and at far less financial cost than the sum currently wasted on roads. Plainly put, such a plan is in every way except reduction in profit to wealthy corporations much fairer, cheaper and more rational than the present transport system. There should be no tolerance (personally or politically) for any policy other than 100 percent of spending on public transport, and not a solitary cent on roads.</p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-8053783179789419522023-07-17T23:29:00.000+10:002023-07-17T23:29:46.431+10:00Consistent failure and consistent silence<p>Probably the most striking and most consistent feature of cricket history — at least since the middle 1890s — has been the failure of English spin bowlers in Australia. This is especially true given their dominance of first-class bowling records.</p><p>Since Bobby Peel and Johnny Briggs in the late 1880s and early 1890s — as will be noted, a wholly unsuitable comparison — <i>no</i> English spin bowler has <i>ever</i> been a matchwinner at Test level in Australia. The universal failure of the most successful county bowlers like Tich Freeman, Wilfrid Rhodes, Colin Blythe, Eric Hollies, Frank Woolley or Richard Tyldesley, plus the fact that an even greater number of extremely successful county bowlers like Charlie Parker, Tom Goddard, George Dennett, Walter Mead, Schofield Haigh, Albert Hallam and Razor Smith were never remotely considered for a tour of Australia, is <i>chilling</i>. Even the less unsuccessful English spinners — Roy Kilner, Jack White, Hedley Verity, Jim Laker, Fred Titmus, Derek Underwood — were never able to win Tests like they consistently won county matches at home. What these relative successes could do was contain batsmen over extremely long spells, a critical skill in the conditions of Test cricket in Australia at the time.</p><p>Statistics demonstrate the abysmal record of English spinners in Australia:</p><p></p><ol style="text-align: left;"><li>since 1905, only <i>twice</i> has an English spinner taken ten wickets in a Test in Australia</li><ol><li>out of more than forty occurrences in all Ashes Tests</li><li>and many more than that elsewhere in international cricket</li></ol><li>no English spinner had taken so many as 26 wickets in a series in Australia since 1903/1904</li><ol><li>whereas as of 1998 (a quarter of a century ago!) this had occurred more than seventy times in all Test cricket</li></ol></ol><div>Both 1903/1904, when Rhodes took thirty-one wickets in five Tests, and the success of Peel and Briggs between 1886 and 1895, reflect abnormal climatic conditions. 1886 to 1894 was the wettest era in the instrumental record in eastern Australia, and in Melbourne 1903/1904 was the wettest and second-coolest summer since records began in 1856. The wet conditions produced pitches much less unfavourable to spin.</div><div><br /></div><div>What is equally striking, analysing both <b><u>Wisden</u></b> and the English and Australian presses, is the complete absence until the 1950s of discussion about English spinners’ abysmal record in Australia. Whenever discussing whom to choose for an Australian tour the failure of English spin was not discussed. Nor was the question ever asked after the most unsuccessful Ashes tours like 1907/1908, 1920/1921, 1924/1925 and 1946/1947. The Australian press was almost equally silent, although it might be expected to have more idea why English spinners were so hopeless. The fact that Australia produced an exceptional number of high-class spinners in this very period constitutes <i>the</i> proof Australian pitches were not impossible for spin bowling.</div><div><br /></div><div>Two obvious reasons are:</div><div><ol style="text-align: left;"><li>the sport-watching public possessed negligible interest in understanding why English spin bowling so consistently failed in Australia</li><li>because of the large number of first-class teams in England, bowlers much better suited to Australian pitches always existed, making the universal failure of English spin into a non-issue</li></ol><div>However, I have recently thought that a more important reason for the silence at least of <b><u>Wisden</u></b> and the English press may be that at a very early point — following Colin Blythe’s complete failure in 1907/1908 — it became accepted that failure of English spinners in Australia was <i>a law of nature</i> and that expecting them to win matches as they did in England was <i>tantamount to tampering with nature</i>. Belief that either:</div><div><ol style="text-align: left;"><li>English spinners could never be trained or coached to emulate their English successes in Australia because their special skills were specific to English conditions and entirely useless in Australia, or</li><li>the cost of making English spinners as effective in Australia as at home would be prohibitive in one or more of:</li><ol><li>labour</li><li>time</li><li>their value at home via either</li><ul><li>reduced success in English conditions</li><li>loss of the art of spin via adopting medium pace in Australia, as Bobby Peel and Freddie Brown did</li></ul></ol></ol><div>fits perfectly with the silence about the abysmal record of English spin in Australia. Belief that English spinners could never be effective in Australia (under normal climatic conditions) would explain why the 1911/1912 and 1920/1921 teams included no player for spin alone, and the surprise of <b><u>Wisden</u></b> at the objectively modest but comparatively exceptional success of Jack White in 1928/1929.</div></div></div><div><br /></div><div>When England’s writers became nostalgic for predominant spin bowling in the 1960s, foreign writers occasionally discussed English spinners’ woeful record in Australia, if without the vehemence with which <b><u>Wisden</u></b> writers criticised current English cricket, and rarely quoting the striking figures noted at the beginning of this post. It is likely that writers in Australia and the West Indies viewed even the very best English spinners as mediocre-to-bad bowlers unimportant to the broader history of cricket. (This, even if accurate, meant they failed to dissect their weaknesses). English writers, for their part, were tied between their nostalgia for prominent spin bowling and the plain fact that English spinners had been matchwinners in Test cricket only at home, and there only before covering was adopted in 1959. In both cases the presumed perspective was highly unfavourable to dissecting and analysing why England could not produce spin bowlers capable of sustained success in Tests under Australian conditions.</div><p></p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-31215863255422557562023-06-20T09:33:00.199+10:002023-12-24T00:12:08.207+11:00Four sub-sequences revealedNotice the following four <i>complete</i> sequences, in which the next number satisfying <b>n</b> after zero is listed if zero satisfies the requirement:<style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:2px;
overflow:hidden;padding:2px 10px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:2px;
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.tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top}
.tg .tg-0lax{text-align:left;vertical-align:top}
</style><table class="tg" style="table-layout: fixed; width: 686px;">
<colgroup>
<col style="width: 76px;"></col>
<col style="width: 76px;"></col>
<col style="width: 76px;"></col>
<col style="width: 76px;"></col>
<col style="width: 76px;"></col>
<col style="width: 46px;"></col>
<col style="width: 46px;"></col>
<col style="width: 46px;"></col>
<col style="width: 46px;"></col>
<col style="width: 46px;"></col>
<col style="width: 76px;"></col>
</colgroup>
<thead>
<tr>
<th class="tg-amwm">0</th>
<th class="tg-amwm">1</th>
<th class="tg-amwm">2</th>
<th class="tg-amwm">3</th>
<th class="tg-amwm">4</th>
<th class="tg-amwm" colspan="2">5</th>
<th class="tg-amwm" colspan="2">6</th>
<th class="tg-amwm" colspan="2">7</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-0lax">104</td>
<td class="tg-0lax">29</td>
<td class="tg-0lax">3</td>
<td class="tg-0lax">5</td>
<td class="tg-0lax">9</td>
<td class="tg-0lax">0</td>
<td class="tg-0lax">1</td>
<td class="tg-0lax" colspan="2">42</td>
<td class="tg-0lax" colspan="2">80562</td>
</tr>
<tr>
<td class="tg-0lax">132</td>
<td class="tg-0lax">31</td>
<td class="tg-0lax">9</td>
<td class="tg-0lax">4</td>
<td class="tg-0lax">3</td>
<td class="tg-0lax" colspan="2">1</td>
<td class="tg-0lax" colspan="2">2054</td>
<td class="tg-0lax">0</td>
<td class="tg-0lax">190783</td>
</tr>
<tr>
<td class="tg-0lax">89</td>
<td class="tg-0lax">21</td>
<td class="tg-0lax">10</td>
<td class="tg-0lax">2</td>
<td class="tg-0lax">5</td>
<td class="tg-0lax" colspan="2">22</td>
<td class="tg-0lax">0</td>
<td class="tg-0lax">1</td>
<td class="tg-0lax" colspan="2">224241</td>
</tr>
<tr>
<td class="tg-0lax">135</td>
<td class="tg-0lax">24</td>
<td class="tg-0lax">6</td>
<td class="tg-0lax">2</td>
<td class="tg-0lax">3</td>
<td class="tg-0lax">0</td>
<td class="tg-0lax">1</td>
<td class="tg-0lax" colspan="2">4</td>
<td class="tg-0lax" colspan="2">211696</td>
</tr>
</tbody>
</table>These four sequences are, in a sense, <i>sub-sequences of <a href="https://oeis.org/A186311">A186311</a></i>. Numbers being each row from the top, we have:<div><ol style="text-align: left;"><li>Least <i>k</i> such that the interval 100<i>k</i> to 100<i>k</i>+99 has exactly <b>n</b> primes ending in 1</li><li>Least <i>k</i> such that the interval 100<i>k</i> to 100<i>k</i>+99 has exactly <b>n </b>primes ending in 3</li><li>Least <i>k</i> such that the interval 100<i>k</i> to 100<i>k</i>+99 has exactly <b>n</b> primes ending in 7</li><li>Least <i>k</i> such that the interval 100<i>k</i> to 100<i>k</i>+99 has exactly <b>n</b> primes ending in 9</li></ol><div>It is easy to see that there can never be more than seven primes ending in the same digit between multiples of 100, as minimally three numbers must divide by 3. When I looked more closely it seemed clear that there could be six primes in a century ending in the same digit, but I was unsure that there could be seven. Brian Kehrig, in a LinkedIn conservation, said there could be and gave the smallest example after the first century (all factorisations courtesy of <a href="https://www.alpertron.com.ar/ECM.HTM">Alpertron</a>, although I have expanded repeated factors rather than use exponents):</div><div><br /></div><span style="color: red;">1. 8056201 is prime<br /></span>
8056203 = 3 × 2 685401<br />
8056207 = 73 × 110359<br />
8056209 = 3 × 7 × 19 × 61 × 331<br /><span style="color: red;">
2. 8056211 is prime<br /></span>
8056213 = 11 × 41 × 17863<br />
8056217 = 13 × 467 × 1327<br /><span style="color: #666666;">
8056219 is prime<br /></span>
8056221 = 3 × 2685407<br />
8056223 = 7 × 47 × 47 × 521<br />
8056227 = 3 × 2685409<br />
8056229 = 29 × 83 × 3347<br /><span style="color: red;">
3. 8056231 is prime<br /></span>
8056233 = 3 × 3 × 3 × 23 × 12973<br />
8056237 = 7 × 7 × 164413<br />
8056239 = 3 × 571 × 4703<br /><span style="color: red;">
4. 8056241 is prime<br /></span>
8056243 = 13 × 619711<br />
8056247 = 19 × 167 × 2539<br />
8056249 = 17 × 31 × 15287<br />
8056251 = 3 × 3 × 7 × 127877<br />
8056253 = 179 × 45007<br />
8056257 = 3 × 11 × 244129<br /><span style="color: #666666;">
8056259 is prime<br /></span><span style="color: red;">
5. 8056261 is prime<br /></span>
8056263 = 3 × 1609 × 1669<br /><span style="color: #666666;">
8056267 is prime<br /></span>
8056269 = 3 × 3 × 13 × 37 × 1861<br /><span style="color: red;">
6. 8056271 is prime<br /></span>
8056273 = 59 × 136547<br /><span style="color: #666666;">
8056277 is prime<br /></span>
8056279 = 7 × 11 × 23 × 4549<br />
8056281 = 3 × 67 × 149 × 269<br />
8056283 = 17 × 473899<br />
8056287 = 3 × 3 × 3 × 29 × 10289<br /><span style="color: #666666;">
8056289 is prime<br /></span><span style="color: red;">
7. 8056291 is prime<br /></span>
8056293 = 3 × 7 × 383633<br /><span style="color: #666666;">
8056297 is prime</span><br />
</div><div><br /></div><div>It’s notable that a(7) for all these sequences lies in the “core” of the “eight-digit gap” where the geometric distance between prime-rich centuries is at a maximum. Within the numbers encompassing these centuries there is no century containing so many as fifteen total primes. The 80,563<sup>rd</sup> century is the 263<sup>rd</sup> with <a href="https://oeis.org/A186405">thirteen total primes</a>, while the 190,784<sup>th</sup>, 211,697<sup>th</sup>, and 224,242<sup>nd</sup> all have too few primes to be similarly counted on OEIS.</div><div><br /></div><div>The possibility of these sequences I observed many years ago when I noticed that all the following numbers were composite:</div><span><ul style="text-align: left;"><li>8907 = 3 × 2969</li><li>8917 = 37 × 241</li><li>8927 = 79 × 113</li><li>8937 = 3 × 3 × 3 × 331</li><li>8947 = 23 × 389</li><li>8957 = 13 × 13 × 53</li><li>8967 = 3 × 7 × 7 × 61</li><li>8977 = 47 × 191</li><li>8987 = 11 × 19 × 43</li><li>8997 = 3 × 2999</li></ul><div>I also noticed at a fairly early stage the unusual factorisations of the 105<sup>th</sup> century:</div><div><br /><span style="color: red;">10401 = 3 × 3467<br /></span>
10403 = 101 × 103<br />
10407 = 3 × 3469<br />
10409 = 7 × 1487<br /><span style="color: red;">
10411 = 29 × 359<br /></span>
10413 = 3 × 3 × 13 × 89<br />
10417 = 11 × 947<br />
10419 = 3 × 23 × 151<br /><span style="color: red;">
10421 = 17 × 613<br /></span>
10423 = 7 × 1489<br /><span style="color: #666666;">1. 10427 is prime<br />2. 10429 is prime<br /></span><span style="color: red;">
10431 = 3 × 3 × 19 × 61<br /></span><span style="color: #666666;">3. 10433 is prime<br /></span>
10437 = 3 × 7 × 7 × 71<br />
10439 = 11 × 13 × 73<br /><span style="color: red;">
10441 = 53 × 197<br /></span>
10443 = 3 × 59 × 59<br />
10447 = 31 × 337<br />
10449 = 3 × 3 × 3 × 3 × 3 × 43<br /><span style="color: red;">
10451 = 7 × 1493<br /></span><span style="color: #666666;">4. 10453 is prime<br />5. 10457 is prime<br />6. 10459 is prime<br /></span><span style="color: red;">
10461 = 3 × 11 × 317<br /></span><span style="color: #666666;">7. 10463 is prime<br /></span>
10467 = 3 × 3 × 1163<br />
10469 = 19 × 19 × 29<br /><span style="color: red;">
10471 = 37 × 283<br /></span>
10473 = 3 × 3491<br /><span style="color: #666666;">8. 10477 is prime<br /></span>
10479 = 3 × 7 × 499<br /><span style="color: red;">
10481 = 47 × 223<br /></span>
10483 = 11 × 953<br /><span style="color: #666666;">9. 10487 is prime<br /></span>
10489 = 17 × 617<br /><span style="color: red;">
10491 = 3 × 13 × 269<br /></span>
10493 = 7 × 1499<br />
10497 = 3 × 3499<br /><span style="color: #666666;">10. 10499 is prime</span><br />
</div></span><div><br /></div>The four A186311 “sub-sequences” are not yet on OEIS, nor is there any OEIS list of centuries with seven primes ending in one of 1, 3, 7, or 9. Given that I would need better software and an OEIS account to add them, the brief discussion here is something I have wanted to do.jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-10665878499237988772023-05-26T20:11:00.237+10:002023-10-27T00:06:06.748+11:00‘Commerce and Coalitions’ II: Cold War-era Southern Africa<p>In <a href="https://jpbenney.blogspot.com/2023/05/a-fascinating-and-revealing-book.html">my previous post</a> on Ronald Rogowski’s <b><u>Commerce and Coalitions</u></b>, I said that I would look at the somewhat peculiar case of Cold War-era Southern Africa and try to apply what I know about that region in that era.</p><p>I will admit I am no expert on Cold War-era Southern Africa, but reading <b><u>Commerce and Coalitions</u></b> it has come to increasingly strike me as a peculiar, even <b><i>sui generis</i></b>, case that Rogowski undoubtedly could have covered with the information he had in 1987 to 1989 when the book was written.</p><p>Following from Thomas Aquinas McMahon in <b><u>Global Runoff: Continental Comparisons of Annual Flows and Peak Discharges</u></b>, we can define Southern Africa politically as Angola, Botswana, Lesotho, Mozambique, Namibia, Rhodesia (now Zimbabwe), South Africa, Swaziland (now Eswatini) and Zambia. By Rogowski’s criteria, the entirety of Southern Africa was (and is) <i>a backward region with very high land/labor ratios</i>, in which only agriculture (and mining) would benefit from free trade. [Malawi (formerly Nyasaland), politically linked to Rhodesia before independence, would qualify as labour-rich, for its uncorrected land/labor ratio is only one-third the lowest in Southern Africa proper.] Under expanding trade, it would be expected that traditionalist politics would come to dominate the region in opposition to the urban sector.</p><p>However, despite Rogowski classifying the Cold War era as a period of trade expansion, this was not applicable to Southern Africa. Rather, the region — excluding Botswana — was during this era dominated by externally imposed sanctions that severely restricted trade. No region has been subject to sanctions to a comparable degree, and apart from Israel no region has had so long a period of collapsing trade in modern times. In fact, omitting regions unexplored or permanently closed off, the prolonged contraction of trade in Cold War-era Southern Africa is unparalleled since the declining Roman Empire. Under a condition of restricted trade, we expect that agriculture and mining would lose ground to the urban sectors of capital and labour.</p><p>Rogowski argues in his discussion of sub-Saharan Africa after World War II (page 117) that the basic political cleavage between the peasantry and the urban sector tended to favour the latter. He gives no examples for Southern Africa, but here the patterns were completely different. In Botswana — both the most land-abundant nation and the only one participating in the postwar expansion of trade — we <i>did</i> observe the predicted landed control of politics and hegemony over capital and labour. As David Ariel Steinberg noted in his 2010 thesis <a href="https://www.proquest.com/openview/59857e5c6933967c78c08e0e28d35fc3/1">‘The Politics of Exchange Rate Valuation in Developing Countries’</a>, Botswana’s politics since independence has been completely dominated by cattle exporters (page 223) with urbanites having no influence. Elsewhere, sanctions imposed by the Eastern bloc and Non-Aligned Movement against the Portuguese <b>Estado Novo</b> (who ruled Angola and Mozambique until 1975), apartheid South Africa and Rhodesia blocked trade, and a completely different pattern prevailed. Whereas capital and labour would have been expected to ally, labour actually became radicalised, and Marxist parties (MPLA, FRELIMO) emerged as the chief opposition to the <b>Estado Novo</b>’s rule. In South Africa and Rhodesia, there was major radicalisation of black workers, and although the illegal Communist Party did not emerge as the focus it did in the <b>Estado Novo</b> colonies, the imprisoned Robert Mugabe was at this stage strongly influenced by Marxism. <a href="https://jpbenney.blogspot.com/2022/12/social-democracy-and-aristocracys.html">Kautsky</a>’s 1968 prediction agrees with Marxist-Leninist parties being strongest in the <b>Estado Novo</b> colonies where the colonial state was closely linked with the Catholic Church, but even elsewhere the militancy of labour is quite different from the eastern areas of the declining Roman Empire, and far beyond what happened in Australia and the Western Hemisphere during the collapse of trade after World War I.</p><p>This radicalisation of workers is unique for a land-rich society, and quite different from the most land-rich parts of the declining Roman Empire (although these were not nearly so relatively land-rich as Southern Africa, and their decline in trade smaller than in the western Empire). The most logical conclusion is that, because the falling trade was driven by external sanctions, workers could <i>identify with the foreign sanctioners</i> rather than the local rulers. This permitted powerful radicalisation in the form of unified internal and external opposition to Southern Africa’s white rulers, and support for continued blocking of trade. Capitalists, rather than moderating the radicalisation of workers, were largely passive. One might conclude that capital and labour did not cooperate because they were racially divided, which further strengthens the case for effectiveness of sanctions whose purpose was to strengthen the ability of blacks to protest against white minority rule.</p><p>Two significant final points:</p><p></p><ol style="text-align: left;"><li>unlike Cold War Southern Africa, even longer-lasting Arab sanctions have affected Israel in the predicted way:</li><ul><li>land in the form of synagogues and rural communes has been strengthened at the expense of Israel’s abundant factors of capital and labour</li><li>Israel very strongly resembles medieval Europe in its response to prolonged declining trade in a capital- and labour-rich, land-poor country — religion and agriculture have been strengthened</li><li>as I noted in my original review, medieval Europe and modern Israel illustrate how powerful religion in a labour-rich society requires isolation from world markets, as otherwise labour will largely eliminate religion’s influence</li></ul><li>similar efforts at sanctions against other land-rich, capital- and labour-poor societies in Iran, Libya, Sudan and Syria have not had the same effect as in Southern Africa. There are several possible reasons for this:</li><ol><li>these nations are less labour-poor and more capital-poor, so sanctions radicalise owners of capital much more than they do owners of labour</li><li>the sanctions have been imposed by fewer countries and thus are less effective at reducing trade (in these cases, few nations have joined the United States in imposing sanctions)</li><li>the political influence of the Gulf States where labour is devoid of political and social rights blocks labour when it gains from reduced exposure to trade</li><ul><li>in this context the Gulf States absorb labour even from relatively land-rich adjacent nations, weakening the organisational ability of those nations’ workers</li></ul></ol></ol><div>Which of the three prevents sanctions being effective probably varies between those four nations, and is beyond the scope of this post.</div><p></p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-34674516898805699162023-05-26T11:20:00.394+10:002023-10-22T13:13:24.955+11:00A fascinating and revealing book despite its age<p>Recently, through an accidental discovery, I have been heavily reading a 1989 book by still-active Professor Ronald Rogowski titled <u><b>Commerce and Coalitions: How Trade Affects Domestic Political Alignments</b></u>.</p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhF-TNHfyn09Ma9-R_V19w-ReqK7uNBHKzP33_96yFmpMhPY3NDqjjxpsAlXXvn8XMkKSgyNlVrzDwinHH70IyrRWEPwC0T7aQa-ElkeDEBVg_FeHFI-a3pqsqMzv4fQehnnvd441WixG6go9lIKkspwRfyKTHAnwTXDbdzqy9mKTD3u16unrB-q3daqXc/s1207/product_pages.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1207" data-original-width="800" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhF-TNHfyn09Ma9-R_V19w-ReqK7uNBHKzP33_96yFmpMhPY3NDqjjxpsAlXXvn8XMkKSgyNlVrzDwinHH70IyrRWEPwC0T7aQa-ElkeDEBVg_FeHFI-a3pqsqMzv4fQehnnvd441WixG6go9lIKkspwRfyKTHAnwTXDbdzqy9mKTD3u16unrB-q3daqXc/s16000/product_pages.jpg" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Ronald Rogowski’s 1989 <b><u>Commerce and Coalitions</u></b> remains a widely-read and very revealing textbook despite its age and absence of updates<br /></td></tr></tbody></table>Rogowski, plainly, argues that trade affects politics by increasing the power of owners of abundant factors, and decreasing the power of owners of scarce factors. Contrariwise, falling trade benefits owners of scarce factors and hurts owners of abundant factors. He also demonstrates that, fundamentally, countries and societies divide in two ways into four groups:<p></p><ol style="text-align: left;"><li>land/labor ratio</li><li>endowment of capital</li></ol><p>Rogowski argues then that political cleavages depend on:</p><ol style="text-align: left;"><li><i>whether capital allies with land or labor</i></li><li>chiefly, whether each group favour freer trade or more restricted trade</li><ul><li>Rogowski only considers cases where trade is restricted <i>endogenously</i> by tariffs or other controls, or <i>unsystematically by dangers to travel</i>. Instances of <i>exogenous</i> trade controls as found with Israel or Cold War-era Southern Africa are not discussed</li></ul></ol><p>Rogowski does a good job of illustrating his conclusions over varying periods since Classical Greece. The details are done well, and the necessary statistics of relation of population to productive land are explained very well. <b><u>Commerce and Coalitions</u></b> illustrates the contrast in development between humid Eurasia on the one hand and the Western hemisphere on the other, with militant socialism being confined to Eurasia. Rogowski argues that socialism cannot ordinarily develop in a land-abundant economy because workers lose economically from expanding trade and will tend towards nationalism and imperialism. Socialism ordinarily develops in labour-abundant economies where workers gain economically from expanding trade and (attempt to) translate this power into expanded political influence at the expense of landowners, mineowners and priesthoods. Rogowski contradicts Karl Marx when he says that militant socialist movements are <i>extremely unlikely in advanced countries</i>, because labour either:</p><ol style="text-align: left;"><li>loses from expanding trade if land-rich or</li><li>is too allied with capital if labour-rich</li></ol><p>Following John Kautsky’s <a href="https://jpbenney.blogspot.com/2022/12/social-democracy-and-aristocracys.html">Social Democracy and the Aristocracy: Why Socialist Labor Movements Developed in Some Countries and Not in Others</a>, one might argue that in advanced labour-rich countries militant socialism can develop via opposition to land, as occurred in northwestern Europe in the late nineteenth century. However, Rogowski may be correct that without a significant priestly power to oppose, worker militancy is unlikely in a labour-rich advanced nation. Rogowski also believes militant socialist movements will fail to develop anywhere during periods of falling trade. This also opposes the predictions of many Marxists who see militant socialism as most likely during economic crises.</p><p>There are some interesting details that are not often heard — for instance how abolitionism in the United States was necessarily linked with protection and how Nazism and Fascism gained their primary support from landowners and peasants who gained via loss of competition from Australia, Africa and the Western Hemisphere.</p><p>Two flaws in the book are that:</p><ol style="text-align: left;"><li>it has not been updated to take into account the expansion of trade following the collapse of Stalinism in Eastern Europe, which was much larger and more widespread than after World War II, and</li><li>owners of <i>mineral</i> resources are largely neglected in favour of owners of farmland, although typically in land-rich economies owners of mines are more intensely affected by changing trade than those of farmland</li><ol><li>in this context one wonders whether land/labor ratios could be adjusted to take into account the abundance of minerals as well as agricultural land</li><li>in most cases this will amplify differences in land endowment, but in a few — for example New Zealand which is very farmland-rich but very mineral-poor — there is opposition and this is extremely tough to quantify</li></ol><li>it ignores that for most of history no regions have been abundant in both capital and land.</li><ul><li>this was the case throughout the period from before the decline of the Roman Empire until the late nineteenth century <br /></li><li>instead of Rogowski’s square-shaped Figure 1.2 (page 8), I would prefer a <i>diamond-shaped spectrum</i> that permits a reduction to the three-way division found in the long sixteenth century and declining Roman Empire of</li><ol><li>capital-rich</li><li>land-rich</li><li>neither capital- nor land-rich<br /></li></ol><li>the book also fails to discuss <i>why</i> capital- and land-rich, labour-poor regions were absent for so long<br /></li></ul></ol><p>In addition to the several questions explained clearly in chapter six, one could add several more questions made easier to answer:</p><ol style="text-align: left;"><li>why negligible religion in humid Eurasia since World War II, and<br />why has secularism triumphed over every religion except Islam (as per <b><u>Be Careful with Muhammad</u></b> by the late Shabbir Akhtar, almost perfectly contemporary with <b><u>Commerce and Coalitions</u></b>)?</li><ol><li>religious institutions — a component of “land” as defined by Rogowski — lose from expanding trade in land-poor societies to workers who minimally resent religion’s power, and at worst see its mythology as primitive superstition holding workers back from political empowerment<br /></li><li>Islam — unlike any other major religion —is based in extremely land-rich Saudi Arabia, and most Muslim nations in Central Asia and North Africa are also very land-rich. Thus rising trade has enriched and strengthened Islamic institutions even as it mortally weakens other religions<br /></li><ul><li>the reactionary character of Christian churches whose power base in Europe was dependent on local agriculture’s isolation from world markets may have prevented Christianity gaining comparable influence in land-rich Australia and the Western Hemisphere</li></ul><li>Rogowski’s thesis implies that religion <i>cannot maintain significant influence in labor-rich societies except under falling trade</i>, as occurred with Christianity in medieval Europe, Buddhism in pre-industrial Asia, and Judaism in Israel today</li></ol><li>following from 1), why extreme isolationism in Tokugawa Japan and Korea during same era:</li><ol><li>these nations were and remain the most land-poor and labor-rich in the world, thus any opening of trade will radicalise owners of labor much more than even in the European cases discussed by Alexander Gerschenkron in <b><u>Economic Backwardness in Historical Perspective</u></b></li><li>the ruling class(es)’ dependence on isolation from world markets was so great that strong states were needed to maintain the desired isolation<br /></li><li>thus, in East Asia, a tradition of strong states was built up before forcible opening to the outside world</li></ol><li>why did the black civil rights movement in the US emerge when it did?</li><ol><li>as James Löwen showed in <b><u>Sundown Towns</u></b>, black Americans were <b>de facto</b> excluded from ownership of the abundant factors of capital and land by local laws effective everywhere in the United States</li><li>expanding trade, by decreasing the value of the only commodity blacks could own — labour — thus weakened black protest capacity and increased the ability of white Americans to discriminate against blacks</li><li>contracting trade thus strengthened black protest capacity by increasing the value of the products of their labour, which under free trade would be imported<br /></li><li>the black civil rights movement can thus be viewed as <i>a delayed by-product of the collapse of world trade following World War I</i>.</li><ul><li>one can argue that the strength of any black civil rights movement is proportional to how rapidly trade declines<br /></li></ul><li>the gains of black Americans were<i> </i>for the great majority largely reversed once trade expanded rapidly — leading to mass incarceration and growing police brutality — further confirming the dependence of even a partly successful black civil rights movement upon isolation from the competition of international trade</li></ol></ol><p>Despite its flaws and lack of updates, <b><u>Commerce and Coalitions</u></b> is a very worthwhile read that makes somewhat mysterious facets of history easily understandable.</p><p>I intend to write two more articles, one interpreting the somewhat peculiar case of Cold War-era Southern Africa and one looking at the problems of capital- and land-rich, labour-poor economies. <br /></p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-186104018262681812023-04-14T23:22:00.165+10:002023-08-21T01:50:09.142+10:00An expected confirmationIn <a href="http://jpbenney.blogspot.com/2023/04/comparing-prime-rich-centuries-part-ii.html">my previous post</a>, I noted that although repeating centuries with fifteen primes <i>are</i> known (although I cannot discover their identity at present) I was sure that they would not occur as early as the 55<sup>th</sup> century with fifteen primes. I discussed this in the context of a repeat of fifteen of seventeen primes from the century from 1,400 to 1,499 in the 55<sup>th</sup> century with <i>seventeen</i> primes (from 1,888,314,999,580,100 to 1,888,314,999,580,199). For both these centuries primes form by adding all numbers within the set {23, 27, 29, 33, 47, 51, 53, 59, 71, 81, 83, 87, 89, 93, 99}.<div><br /></div><div>Tonight I have actually computed the prime patterns for all centuries with fifteen primes less than one billion. There are 58 centuries smaller than one billion with fifteen primes, and fifteen is the largest number of primes in any century within the “eight-digit gap”, which extends from slightly below three million to 839,296,299. (This “eight-digit gap” is partly predictable from heuristics. Around this digit count the rate at which the probability of a century containing more the fifteen primes decreases equals the inverse of the rate at which the number of centuries increases, although the lowest theoretical probabilities of the existence of any century with sixteen or seventeen primes actually occur for <i>seven</i> digits).</div><div><br /></div><div>As I strongly expected, none of the first fifty-eight centuries with fifteen primes have the same pattern. In fact, of the 1,653 possible pairs from these first fifty-eight centuries with fifteen primes, no pair forms common primes by adding a set larger than twelve numbers, and only four have this number of common primes.</div><div><br /></div><div>It is too cumbersome and impractical to list the patterns of all 58 centuries; however, I will list the number of common primes for each pair:</div><br />
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.tg .tg-69bx{background-color:#656565;color:#ffffff;text-align:left;vertical-align:bottom}
</style>
<table class="tg">
<thead>
<tr>
<th class="tg-j6zm"># same primes</th>
<th class="tg-j6zm"># centuries to 1 billion</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
<td class="tg-usyp"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">1</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">2</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">66</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">3</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">147</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">282</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">5</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">260</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">6</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">190</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">7</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">196</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">8</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">205</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">9</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">170</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">10</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">96</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">11</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">22</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">12</span></td>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">4</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">13</span></td>
<td class="tg-usyp"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-7zrl"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">14</span></td>
<td class="tg-usyp"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
<tr>
<td class="tg-69bx"><span style="font-style: normal; font-weight: 400; text-decoration: none;">15</span></td>
<td class="tg-usyp"><span style="color: black; font-style: normal; font-weight: 400; text-decoration: none;">0</span></td>
</tr>
</tbody>
</table>
The four pairs of centuries with twelve common primes are, in order of smallest larger century:
<div><ol style="text-align: left;"><li><b>6,300 to 6,399</b> and <b>2,967,300 to 2,967,399</b> with common primes formed by adding {17, 23, 29, 37, 43, 53, 59, 61, 73, 79, 89, 97}</li><li><b>46,497,700 to 46,497,799</b> and <b>593,131,900 to 593,131,999</b> with common primes formed by adding {7, 9, 19, 27, 33, 39, 51, 61, 67, 91, 93, 97}</li><li><b>516,257,800 to 516,257,899</b> and <b>738,740,200 to 738,740,299</b> with common primes formed by adding {1, 3, 9, 13, 21, 51, 57, 69, 79, 81, 91, 93}</li><li><b>2,600 to 2,699</b> and <b>925,594,400 to 925,594,499</b> with common primes formed by adding {9, 33, 47, 57, 59, 63, 71, 77, 87, 89, 93, 99}</li><ul><li>both these last two are part of extremely prime-rich sequences that overlap two centuries:</li><ul><li>the century from 2,650 to 2,750 contains <i>eighteen primes</i></li><li>the century between 925,594,420 and 925,594,520 contains <i>seventeen primes</i></li><ul><li>in fact all these seventeen primes are between 925,594,429 and 925,594,513 (85 numbers)</li><li>yet, there is no case of so many as seventeen primes between consecutive multiples of 100 amongst nine- or even ten-digit numbers</li></ul></ul></ul></ol><div>Overall, there is nothing amongst the fifteen-prime centuries less than one billion to compare with the similarity of the prime patterns of the centuries beginning with 1,400 and 1,888,314,999,580,100. This is what I expected. Even taking into account that there are more than four times as many possible prime patterns for a fifteen-prime as for a seventeen-prime century, I had no expectations of something closer to a repeating century than the four cases mentioned above.</div></div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-54484068284396386292023-04-13T21:58:00.105+10:002023-08-08T01:02:09.777+10:00Comparing the prime-rich centuries: Part II<p>In <a href="http://jpbenney.blogspot.com/2023/02/comparing-prime-rich-centuries.html">my previous post</a>, I compared the first few seventeen- and eighteen-prime centuries to see what their patterns were like.</p><p>Most of the smallest seventeen- and eighteen-prime centuries, as noted in that post, are of the form 100<b>k</b> to 100<b>k</b>+99 where <b>k</b> is a number of the form 3<b>n</b>+1. This is not unexpected. A century from 300<b>n</b>+100 to 300<b>n</b>+199 contains <i>28</i> numbers not divisible by 2, 3, or 5, whereas a century from 300<b>n</b> to 300<b>n</b>+99 or from 300<b>n</b>+200 to 300<b>n</b>+299 contains only <i>26</i> numbers not divisible by 2, 3, or 5. (Divisibility by 7, however, means no century can contain so many as 26 prime numbers: indeed, the maximum number of primes any century after the first can theoretically contain is 23, and no century larger than the second is known to contain more than 20 primes).</p><p>As noted in the previous post about prime-rich centuries, the <i>second</i> seventeen- and the <i>second</i> eighteen-prime centuries have <b>k</b> of the form 3<b>n</b>+2. The next seventeen-prime century with <b>k</b> of the form 3<b>n</b>+2 or 3<b>n</b> is the sixteenth overall and the first seventeen-prime century after than the smallest eighteen-prime one. This century — from 190,818,931,155,800 to 190,818,931,155,899 — is also <i>the first century after 1,400 to 1,499 with a single-digit count of composite numbers not divisible by 2, 3, or 5</i>.</p><p>Below the second eighteen-prime century from 2,335,286,971,401,800 to 2,335,286,971,401,899 (actually alongside the prime number 2,335,286,971,401,799 there are nineteen primes in 101 numbers) there are:</p><p></p><ul style="text-align: left;"><li>five centuries with seventeen primes and <b>k</b> of the form 3<b>n</b>+2</li><li>six centuries with seventeen primes and <b>k</b> of the form 3<b>n</b></li></ul><div>I will tabulate these twelve centuries as two tables of six centuries each, and compare their prime patterns as I did for the centuries with <b>k</b> of the form 3<b>n</b>+1.</div><p></p>
<h2 style="text-align: left;">First Five Seventeen-Prime Centuries and First Eighteen-Prime Century with <b>k</b> of form 3<b>n</b>+2</h2>
<style type="text/css">
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.tg .tg-fymr{border-color:inherit;font-weight:bold;text-align:left;vertical-align:top}
.tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top}
.tg .tg-8nxe{background-color:#7F7F7F;border-color:inherit;color:#FFF;text-align:left;vertical-align:top}
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<table class="tg" style="table-layout: fixed; width: 996px;">
<colgroup>
<col style="width: 166px;"></col>
<col style="width: 166px;"></col>
<col style="width: 166px;"></col>
<col style="width: 166px;"></col>
<col style="width: 166px;"></col>
<col style="width: 166px;"></col>
</colgroup>
<thead>
<tr>
<th class="tg-fymr">14</th>
<th class="tg-fymr">1908189311558</th>
<th class="tg-fymr">6157376214122</th>
<th class="tg-fymr">18883149995801</th>
<th class="tg-fymr"><span style="color: black;">22930638581651</span></th>
<th class="tg-fymr">23352869714018</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,803</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,203</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,103</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,103</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,803</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,409</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,209</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,109</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,809</span></td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,211</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,111</span></td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,817</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,217</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,117</span></td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,821</span></td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,121</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,821</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,423</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,823</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,223</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,123</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,123</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,823</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,427</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,227</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,127</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,827</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,429</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,229</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,129</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,829</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,433</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,833</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,233</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,133</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,133</span></td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,439</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,239</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,139</span></td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,841</span></td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,141</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,841</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,447</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,247</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,147</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,147</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,847</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,451</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,851</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,151</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,851</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,453</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,253</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,153</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,153</span></td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,857</span></td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,459</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,859</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,159</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,159</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,859</span></td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,863</span></td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,863</span></td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,869</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,269</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,169</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,169</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,869</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,471</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,871</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,271</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,171</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,871</span></td>
</tr>
<tr>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,177</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,877</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,481</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,281</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,181</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,181</span></td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,483</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,883</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,283</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,183</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,883</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,487</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,887</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,187</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,187</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,887</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,489</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,889</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,289</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,189</span></td>
<td class="tg-8nxe"><span style="color: white;">2,293,063,858,165,189</span></td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,889</span></td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,493</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,893</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,193</span></td>
<td class="tg-0pky"> </td>
<td class="tg-0pky"> </td>
</tr>
<tr>
<td class="tg-8nxe"><span style="color: white;">1,499</span></td>
<td class="tg-8nxe"><span style="color: white;">190,818,931,155,899</span></td>
<td class="tg-8nxe"><span style="color: white;">615,737,621,412,299</span></td>
<td class="tg-8nxe"><span style="color: white;">1,888,314,999,580,199</span></td>
<td class="tg-0pky"> </td>
<td class="tg-8nxe"><span style="color: white;">2,335,286,971,401,899</span></td>
</tr>
</tbody>
</table>
Here, there seems more variation in the patterns than for the more numerous seventeen-prime centuries of the form 3<b>n</b>+1. Nevertheless, there is the remarkable century from 1,888,314,999,580,100 to 1,888,314,999,580,199 that has <i>fifteen primes with identical last two digits to primes between 1,400 and 1,499</i>! Given that there are 2,829,786 possible prime patterns for a century with seventeen primes, and that no repeating patterns with 17 primes are yet known, this is extraordinary since the larger century is merely the fifty-fifth containing seventeen prime numbers. <a href="https://www.mersenneforum.org/showpost.php?p=597063&postcount=5">At least one repeating century with fifteen primes is known</a>, although I remain unaware of its identity, and it certainly does not occur as early as the 55<sup>th</sup> century with 15 primes [<span style="white-space: pre-wrap;">856,019,600 to 856,019,699</span>].<br /><h2 style="text-align: left;">First Six Seventeen-Prime Centuries with <b>k</b> of form 3<b>n</b></h2>
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<thead>
<tr>
<th class="tg-fyfk"><span style="background-color: white; color: black;">7658205745776</span></th>
<th class="tg-9hzb"><span style="background-color: white; color: black;">8078877131667</span></th>
<th class="tg-9hzb"><span style="background-color: white; color: black;">10137710652198</span></th>
<th class="tg-amwm">13862924841999</th>
<th class="tg-amwm">17176990713081</th>
<th class="tg-amwm">19441702516473</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,601</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,701</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,901</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,607</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,707</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,807</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,907</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,307</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,711</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,811</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,911</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,111</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,311</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,613</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,713</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,813</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,913</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,113</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,313</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,817</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,317</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,719</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,819</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,919</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,119</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,623</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,823</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,923</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,123</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,629</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,929</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,329</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,731</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,831</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,131</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,637</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,837</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,937</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,137</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,741</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,841</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,941</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,141</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,341</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,943</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,343</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,647</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,147</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,347</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,649</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,749</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,849</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,149</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,753</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,853</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,153</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,353</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,659</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,759</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,859</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,359</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,661</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,161</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,361</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,767</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,967</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,167</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,367</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,671</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,771</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,971</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,673</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,873</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,173</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,373</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,677</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,777</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,877</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,977</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,177</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,679</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,879</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,979</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,179</span></td>
<td class="tg-0lax"> </td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,683</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,783</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,983</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,183</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,383</span></td>
</tr>
<tr>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,789</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,889</span></td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,989</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,389</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,691</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,791</span></td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,386,292,484,199,991</span></td>
<td class="tg-i2mf"><span style="color: white;">1,717,699,071,308,191</span></td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,391</span></td>
</tr>
<tr>
<td class="tg-i2mf"><span style="color: white;">765,820,574,577,697</span></td>
<td class="tg-i2mf"><span style="color: white;">807,887,713,166,797</span></td>
<td class="tg-i2mf"><span style="color: white;">1,013,771,065,219,897</span></td>
<td class="tg-0lax"> </td>
<td class="tg-0lax"> </td>
<td class="tg-i2mf"><span style="color: white;">1,944,170,251,647,397</span></td>
</tr>
</tbody>
</table>
This list seems, on the whole, more random than either list previously considered. No pair of these six centuries has more than thirteen common primes (807,887,713,166,700 and 1,013,771,065,219,800), which does not seem surprising. There is:<div><ul style="text-align: left;"><li>one pair of last two digits (<b>k</b>13) that is prime for all six</li><ul><li>the same as for the first ten centuries with eighteen primes and ten composites not divisible by 2, 3, or 5</li></ul><li>one pair of last two digits (<b>k</b>43) with only two primes</li><ul><li>the minimum in the centuries mentioned in the preceding point is three</li></ul></ul></div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-29782967663716122112023-02-11T11:30:00.097+11:002023-08-08T01:04:56.841+10:00Comparing the prime-rich centuries<p>I have always had an extremely strong interest in prime numbers — most likely because of the sense of order prime and prime factor tables provide.</p><p>From the time I saw the “First One Hundred Prime Numbers” in my old <b><u>Mathematics Around Us: Skills and Applications</u></b> book I had in school in the 1980s, I have always been interested in memorising prime tables as high as I have. In practice, I have not memorised my prime numbers and factors above the second millennium, although I do remember many primes in later millennia.</p><p>Over the past couple of years, I have discovered that the apparent lack of extremely prime-rich centuries above the century from 2,704,900 to 2,704,999 (which contains seventeen primes) actually does not apply for extremely large numbers. No eight-digit century contains more than fifteen primes and only six contain that many, but so early as 1904, American mathematician Leonard Eugene Dickson predicted that there must exist larger centuries with more than fifteen primes. After 2,704,900 there are none until the sixteen-prime century from 839,296,300 to 839,296,399 — 2.49175625272 orders of magnitude larger in base 10 and 5.73748080288 orders larger in base <b>e</b>. Evidence for Dickson’s Conjecture can however be seen in there being 26 nine-digit centuries, 37 ten-digit centuries, and over 100 eleven-digit centuries containing fifteen primes.</p><p>Another notable discovery is the existence of centuries with <i>eighteen</i> primes — predicted by Dickson in 1904 but not discovered until much later (I have no knowledge of when the first eighteen-prime century was discovered). Early writings about primes in centuries do not note Dickson’s work, but equally do not say that larger centuries with more primes than then-known centuries after the first two cannot exist.</p><p>The high density of primes in these recently discovered prime-rich centuries has made me want to compile them to remember the patterns of primes. Doing so is not easy in a prime-rich sequence of large numbers because there are so many unpredictable patterns of digits to remember — although some of the relevant centuries, like the fifth seventeen-prime century’s <b>k</b> of 144,997,771, do have a pattern that does aid memory a little. So I have decided to tabulate the first eleven seventeen- and eighteen-prime centuries. The second century in each sequence, however, has been excluded because <b>k</b> (the multiple of 100 beginning the century under examination) is not of the form 3<b>n</b>+1 as all the other first eleven seventeen- and eighteen-prime centuries are, but of the form 3<b>n</b>+2. Centuries where <b>k</b> is of the form 3<b>n</b>+2 (or 3<b>n</b>) contain two fewer numbers not divisible by 2, 3, or 5 than centuries where <b>k</b> is of the firm 3<b>n</b>+1 — hence they would require more numbers to properly tabulate and are much harder to compare with other centuries being examined.</p>
<h2 style="text-align: left;">First Eleven Centuries (excluding 1,400 to 1,499) with Seventeen Primes</h2>
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<col style="width: 111px;"></col>
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<tr>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">4</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">7837</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">27049</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">144997771</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">651186838</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">12779564974</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">22369949923</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">149621468452</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">225012717952</span></th>
<th class="tg-j6zm"><span style="color: black; font-size: x-small; font-style: normal; text-decoration: none;">240728320642</span></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">401</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,701</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,901</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,401</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,301</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,201</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,201</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,703</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,903</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,803</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,303</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,707</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,907</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,107</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,807</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,407</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,307</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,207</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,207</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">409</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,909</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,109</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,809</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,409</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,209</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,209</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,209</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,113</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,813</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,413</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,313</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,213</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,213</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,213</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">419</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,719</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,119</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,319</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,219</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">421</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,721</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,121</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,321</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,221</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,221</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,927</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,427</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,327</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,227</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,227</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,227</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">431</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,931</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,431</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,231</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,231</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">433</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,733</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,133</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,233</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,737</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,937</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,137</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,837</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,437</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,237</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,237</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">439</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,939</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,439</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,339</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">443</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,743</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,943</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,143</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,843</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,243</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,243</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">449</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,749</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,849</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,449</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,249</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,151</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,451</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,251</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,251</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">457</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,957</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,857</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,457</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,357</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,257</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,257</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">461</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,161</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,361</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">463</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,763</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,963</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,163</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,863</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,463</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,363</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">467</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,767</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,167</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,867</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,367</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,267</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,969</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,169</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,369</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,269</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,473</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,373</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,273</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,273</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,273</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">479</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,779</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,979</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,179</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,879</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,479</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,279</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,279</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,279</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,781</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,981</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,181</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,881</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,481</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,381</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,281</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,281</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">487</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,787</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,987</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,887</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,487</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,287</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,287</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,287</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">491</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,791</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,191</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,891</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,391</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,291</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,291</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,291</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,793</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,993</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,893</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,293</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,293</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,293</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,704,997</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,499,777,197</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,897</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">1,277,956,497,497</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">22,501,271,795,297</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,297</span></td>
</tr>
<tr>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">499</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">783,799</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">65,118,683,899</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">2,236,994,992,399</span></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">14,962,146,845,299</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-kxp2"><span style="background-color: #757171; color: white; font-size: x-small; font-style: normal; font-weight: 400; text-decoration: none;">24,072,832,064,299</span></td>
</tr>
</tbody>
</table>
One might note that there is a fairly random list of numbers being prime in these ten centuries. As one might expect, a higher proportion of the larger centuries (excluding those beginning with 400, 783,700 and 2,704,900) consists of very large constellations of primes. I noticed this very clearly in the century beginning with 65,118,683,800 (the sixth century containing seventeen primes) that most of the primes were two very large constellations including a prime quadruple, and this is more marked for some of the bigger centuries.<h2 style="text-align: left;">First Eleven Centuries (excluding 2,335,286,971,401,800 to 2,335,286,971,401,899) with Eighteen Primes</h2>
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<table class="tg">
<thead>
<tr>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">1228537713709</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">28703737474266</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">144785865481702</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">161394923966449</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">168975708209638</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">174748809066898</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">207552241231357</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">278215179205531</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">312303328909720</span></th>
<th class="tg-j6zm"><span style="color: black; font-family: inherit; font-size: x-small;">592248982143877</span></th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,901</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,601</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,901</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,801</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,101</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,001</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,701</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,903</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,203</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,803</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,803</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,703</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,103</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,003</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,907</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,607</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,907</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-im72"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,707</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,107</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,707</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,609</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,209</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,909</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,809</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,809</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,709</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,109</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,009</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,709</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,613</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,913</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-im72"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,713</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,013</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,713</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,919</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,219</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,919</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,819</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,921</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,621</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,221</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,921</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,821</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,821</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,721</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,121</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,021</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,721</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,927</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,627</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,827</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,827</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,727</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,127</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,027</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,931</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,231</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,931</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,831</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,131</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,031</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,933</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,633</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,933</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,937</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,237</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,937</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,837</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,737</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,839</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,839</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,739</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,739</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,643</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,243</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,943</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,843</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,143</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,043</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,743</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,949</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,249</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,849</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,849</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,749</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,951</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,651</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,951</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,851</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,751</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,151</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,051</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,657</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,257</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,857</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,157</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,057</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,757</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,961</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,661</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,961</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,861</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,761</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,263</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,963</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,863</span></td>
<td class="tg-im72"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,763</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,163</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,063</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,267</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,867</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,867</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,767</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,167</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,767</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,969</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,669</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-im72"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,769</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,169</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,069</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,769</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,973</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,673</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,273</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,973</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,873</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,873</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,773</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,173</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,073</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,679</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,279</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,979</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,879</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,879</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,779</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,079</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,779</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,281</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,881</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,781</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,781</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,987</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,687</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,287</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,887</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,887</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,787</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,187</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,087</span></td>
<td class="tg-7zrl"><br /></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,991</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,691</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,291</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,891</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,891</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,791</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,191</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,091</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,791</span></td>
</tr>
<tr>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,693</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,293</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,993</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,893</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,893</span></td>
<td class="tg-gvye"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,193</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,793</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,997</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,997</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,897,570,820,963,897</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">17,474,880,906,689,897</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">20,755,224,123,135,797</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">27,821,517,920,553,197</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,097</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,797</span></td>
</tr>
<tr>
<td class="tg-6odw"><span style="color: white; font-family: inherit; font-size: x-small;">122,853,771,370,999</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">2,870,373,747,426,699</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">14,478,586,548,170,299</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">16,139,492,396,644,999</span></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-7zrl"><br /></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">31,230,332,890,972,099</span></td>
<td class="tg-86mj"><span style="color: white; font-family: inherit; font-size: x-small;">59,224,898,214,387,799</span></td>
</tr>
</tbody>
</table>
This table — more difficult to write up than for the seventeen-prime centuries because Excel cannot calculate large enough numbers — is rather odd because there seems to be a pattern of presence and absence in the first eighteen-prime centuries:<div><ul style="text-align: left;"><li><b>k</b>21 is always present as a prime</li><li><b>k</b>73 is present in the first nine</li><li><b>k</b>91 is only missing from one of these centuries</li><li>contrariwise, <b>k</b>19, <b>k</b>33, <b>k</b>39 and <b>k</b>81 are missing from a majority of these centuries</li></ul><div>What these results suggest I am not sure, but there may be some restrictions on prime patterns for centuries with eighteen primes that are not calculated in conventional theories. However, I have no evidence in tables or discussions that this is the case, so the variations may be mere coincidence.</div></div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-81113364765912098472022-12-24T17:38:00.407+11:002023-10-16T11:48:56.758+11:00‘Social Democracy and the Aristocracy’’s insufficient attention to race<p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglTyk3BHaAWBvnYMjuNjZ1WiP6PGqbadizUuvtaXAngQz7MYL9m8GjhYYaBPLVUjuBGyOHhIeE71YC_1Cdb_HrydKkNgDQ1U5lFy9Y7DANnT-yZiRLb7srmIPk1qDgwdIqtS82lBjZhgyU6oc9EeGKLkO9r7KSb7htZROyxdhPxUaI1stadoEACMpX/s1807/social-democracy-and-the-aristocracy.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1807" data-original-width="1200" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglTyk3BHaAWBvnYMjuNjZ1WiP6PGqbadizUuvtaXAngQz7MYL9m8GjhYYaBPLVUjuBGyOHhIeE71YC_1Cdb_HrydKkNgDQ1U5lFy9Y7DANnT-yZiRLb7srmIPk1qDgwdIqtS82lBjZhgyU6oc9EeGKLkO9r7KSb7htZROyxdhPxUaI1stadoEACMpX/w426-h640/social-democracy-and-the-aristocracy.jpg" width="426" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><u><b>Social Democracy and the Aristocracy</b></u>, by the late John Kautsky and originally published in the late 1960s, is an interesting read especially with later additions but is severely flawed by failing to seriously <i>discuss</i> questions concerning race, religion and resource endowment<br /></td></tr></tbody></table>In recent days I have looked at one book originally published as early as the late 1960s but comprehensively revised in the early 2000s — John H. Kautsky’s <u><b>Social Democracy and the Aristocracy: Why Socialist Labor Movements Developed in Some Countries and Not in Others</b></u>.<p></p><p><u><b>Social Democracy and the Aristocracy</b></u>, in the plainest and simplest terms, argues that the social democratic movements of Western Europe and Japan occurred because of struggles, not against the capitalist ruling classes, but against the aristocratic landowning ruling classes. It argues that in North America, and in many modern emerging economies like Brazil, post-Stalinist Russia, Mexico and India, social democratic movements cannot emerge because old ruling aristocracies had been largely eliminated by earlier revolutions.</p><p>Kautsky’s idea is interesting and certainly does make some sense. The hostility of the socialist working classes of Europe was <i>always</i> directed more at the traditional churches than at the capitalists, even if this was because they understood that Christianity was inherently opposed to rights for workers and served a critical role protecting private property. Kautsky demonstrates that the churches did nothing whatsoever to cater to the workers and this left them without the sense of belonging to a community they possessed as peasants. This led the workers of Europe to form socialist parties dedicated to radical social change, especially the overthrow of the old aristocracy.</p><p>Contrariwise, <u><b>Social Democracy and the Aristocracy</b></u> argues that in societies that were “modernised from above” — which encompasses all of Africa, Asia and Latin America except Japan, and also all (ex)-Stalinist nations — the absence of an aristocracy meant that workers identified themselves with the modernising regimes. Kautsky also argues that globalisation — which has made capital mobile without increasing the mobility of labour — means it is unlikely that socialist parties can achieve what they did in Europe during the first two thirds of the twentieth century.</p><p>Kautsky argues that an aristocracy was also absent in the United States and Canada, but he lets himself down here. Many writers since Charles Beard a century and a decade ago have recognised the United States as a fundamentally aristocratic society, albeit one where the <i>white workers were</i> (or merely saw themselves as) <i>part of the aristocracy</i>. Under this condition, the white workers allied themselves with the ruling class against the black minority. Because the ruling classes knew very well that having white workers as allies would both permit much greater exploitation of blacks and protect against the dangers free blacks have always been seen (and still <i>are</i>) as posing the US capitalist system. Plainly said, if free blacks are excluded from (almost) every job, political activism becomes <i>the</i> logical alternative, and having the white masses as allies constitutes perfect insurance against this threat. In <i>Canada</i> and <i>Australia</i> race was also undoubtedly important in limiting radical politics. Until the 1960s Canada and Australia (alongside the Midwest and Northwest of the United States) were <i><b>Herrenvolk</b> democracies</i> that excluded non-whites from settlement or (with remaining native peoples) political participation. In a <b>Herrenvolk</b> state, genuine socialism <b>ipso facto</b> reduces the social status of the electorate so will invariably be rejected. Nevertheless, <u><b>Social Democracy and the Aristocracy</b></u> never considers this, nor any other racial questions.</p><p><u><b>Social Democracy and the Aristocracy</b></u> can also be flawed for its limited focus on <i>religion</i>. One can deduce that the radical anti-religion attitudes of European working classes were critical in developing mass socialist labor parties, for the simple reason that traditional religions invariably used the ruling classes to legitimise them. <i>Ireland</i> — the one northern or western European nation without a mass social democratic labour party — demonstrates conclusively that where religion possesses a critical role in a nation’s founding, the lower classes will support that religion and consequently cannot develop a socialist labour party. The same argument can be applied to the United States and Canada, where many communities were created by religious groups fleeing persecution in Europe. The hypothesis that anti-religious lower classes are critical for social democratic labor parties is supported even more firmly by <i>the Gulf States</i>, which have experienced <i>no democratisation movement whatsoever</i>. These states were modernised from within by Muslim royal ruling classes, who made their citizen populations into a privileged caste segregated from an expatriate (mainly South and East Asian) underclass and a highly skilled Western expatriate middle class. This three-way division of the nonelites in the Gulf States, alongside the deep religious attachment of their citizen populations, has allowed their ruling classes to give capital essentially unlimited power over labour. In exceptionally resource-rich lands that without absolute rule of capital over labour would have probably the highest wages in the world, unions and strikes are completely forbidden and expatriate workers can be fired without restrictions. This unlimited power of capital has created societies powerful enough to severely reduce the global power of labour and immune to externally-driven political challenges.</p><p>Another problem with <u><b>Social Democracy and the Aristocracy</b></u> is the absence of discussion of <i>resources</i>. It has long occurred to me that the ability of Europe, Japan and New Zealand to develop social democracy could be caused by their poverty in natural resources. Owing to the impact of the orogeny of the Alps in the south and repeated glaciations in the north and the Alps, Europe has been stripped of almost all critical mineral resources. Similar analyses apply to Japan and New Zealand. This is most especially true of the high-technology lithophile elements that a preindustrial society is incapable of using and exhausting — the mineral resources that do exist in young, glaciated landscapes are precisely those which a preindustrial society can exploit, but which are most easily exhausted. Especially since reading <a href="https://solidarity-us.org/pdfs/cadreschool/fws.brenner.pdf">Aaron Brenner’s review of Michael Goldfield’s The Color of Politics</a>, I have imagined that, in opposition to Brenner’s quote that</p><blockquote><p style="text-align: center;">“...race becomes the <b>deus ex machina</b> that floats through history explaining the successive failures of working-class struggle. He [Michael Goldfield] is forced into this largely because he dismisses all the other explanations for American exceptionalism offered by the left since Marx. While some may be worthy of dismissal, others are not: the historic strength of American capital, the social and political force of agrarians...”<br /></p></blockquote>natural resource poverty might be what permitted strong social democratic movements in Europe, Japan and New Zealand. Lack of the illiquid, geographically fixed wealth provided by minerals should undoubtedly limit the power of capital and prevent it from dividing labour as it can so easily do in the United States. The absence of social democratic labour parties anywhere in the tropics or arid subtropics is fully in accord with this view because those regions have been too hot for glacial stripping of their minerals, although one might note that there are a number of genuinely resource-poor low-latitude nations that have been modernised from without, like Hong Kong and Taiwan. (One could argue that the modernisation of the “Asian Tigers” was deliberately done in such a manner to prevent powerful socialist labor parties developing).<br /><div><br /></div><div>A fourth fault is that Kautsky sees Leninism and the Russian Revolution as wholly irrelevant to social democracy in industrialised nations, but ignores the internationalism of the Russian Revolution entirely, and also the close connection between the social democratic parties and revolutionary workers’ parties. The workers who would later support social democratic parties frequently supported the extension of the Russian Revolution to Germany and beyond, and almost all admired the Bolsheviks for their ostensible prioritisation of the welfare of the lower classes.</div><div><br /></div><div>All these features seriously flaw <u><b>Social Democracy and the Aristocracy</b></u>, although I found it very much worth the read I gave it in the State Library of Victoria.</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-24723675939023102972022-12-08T21:50:00.186+11:002022-12-21T14:13:58.123+11:00AstroDataBank’s AstroSignatures and possible minimaWhen I read the old (<a href="https://web.archive.org/web/20050208122237/http://www.astrodatabank.com/">now archived</a>) AstroDataBank astrology site during the 2000s, the site’s president Mark McDonough wrote studies of excess and lack of <a href="https://web.archive.org/web/20050404192520/http://astrodatabank.com/AS/ASFire.htm">fire</a>, <a href="https://web.archive.org/web/20050404191947/http://astrodatabank.com/AS/ASEarth.htm">earth</a>, <a href="https://web.archive.org/web/20050404002341/http://www.astrodatabank.com/AS/ASAir.htm">air</a> and <a href="https://web.archive.org/web/20050404193043/http://astrodatabank.com/AS/ASWater.htm">water</a> (with water, McDonough did another later study <a href="https://web.archive.org/web/20070202100035/http://www.astrodatabank.com/ASEveryAstrologerAResearcher.htm">archived here</a>).<div><br /></div><div>I found the studies fascinating at the time; however, I noticed some serious problems.
If you look at the tables for <i>lack</i> of <a href="https://web.archive.org/web/20050404202723/http://astrodatabank.com/AS/ASFire_TblLack.htm">fire</a>, earth (available only as <a href="https://web.archive.org/web/20010303021643/http://astrodatabank.com:80/ASEarth_TblLack.htm">an early achived post</a> dating from before I began to read the site), <a href="https://web.archive.org/web/20041214032903/http://astrodatabank.com/AS/ASAir_TblLack.htm">air</a> and <a href="https://web.archive.org/web/20050404203459/http://astrodatabank.com/AS/ASWater_TblLack.htm">water</a>, you will see that numerous public figures are listed as having <i>a lack of all four elements</i>. This is, of course, <i>logically impossible</i> as planets must be in signs or houses of at least one element.<div><br /></div><div>When I read the original AstroDataBank, I noticed also that there were exceptionally few people other than those obviously errant (as discussed in the preceding paragraph) entirely lacking <i>fire</i>. The following table of all non-errant people listed in the tables from the preceding paragraph should illustrate this. [Biographies are given directly from the original without any alteration due to spelling errors or dialectical variations, while colours are listed as the opposite of the “common” colour of the absent element]
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<th class="tg-g7sd"><span style="color: black;">Name</span></th>
<th class="tg-g7sd"><span style="color: black;">Element</span></th>
<th class="tg-g7sd"><span style="color: black;">Biography</span></th>
<th class="tg-g7sd"><span style="color: black;"><a href="https://www.astro.com/astro-databank/Help:RR">RR</a></span></th>
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<td class="tg-8wvm"><span style="color: white;">Aaron, Dave</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American UFO researcher. Owner of largest inventory in the world of UFO videos (25,000 hours) and tapes (6,000 hours) which he sell from his home office in Yucaipa, CA, the UFO Audio-Video Clearing House, established c. 1990. He supplies videos of alleged UFOs to films and TV. Footage was released on major TV networks in Hong Kong, Japan, Australia, England and U.S. on the Alien Autopsy 8/28/1995, 8-10' film footage that claims to show autopsies of several aliens that crashed in NM. He had an UFO sighting in 1965 when his dad called him outside to see a radiant disk that had landed. When he approached, a beam of light burned his chest, leaving a scar. Formerly married</span></td>
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<td class="tg-40k6"><span style="color: white;">Aavikko, Armi</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Finnish Beauty Queen, a singer and model.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
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<td class="tg-40k6"><span style="color: white;">Aimee, Anouk</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French actress with a film debut in 1947, a hauntingly beautiful brunette, feline, graceful. The daughter of theatrical parents, she studied dance at Opera of Marseilles, followed by drama lessons in Paris. She was highly acclaimed in "Les Amants de Verone", 1949.<br /><br />With little interest in fame she made few films, which including "La Dolce Vita," 1959, "Tragedy of a Ridiculous Man," 1981 and "A Man and a Woman" at the height of her career, 1966. Of her five marriages, the fourth was to British actor Albert Finney 8/07/1970.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
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<td class="tg-8wvm"><span style="color: white;">Albertini, Giampiero</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Italian voice-over actor who dubbed Peter Falk's voice for the TV series "Colombo" in Italy. Died of a heart attack 5/13/91.</span></td>
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<td class="tg-40k6"><span style="color: white;">Ali, Muhammad</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American light-heavyweight gold medallist, the only man to win the heavyweight championship of the world three times. He began boxing professionally on 10/29/1960 and became world champ in 1964 by knocking out Sonny Listen. His title was declared vacant after he refused military obligation as a Moslem because he was a conscientious objector. Ali later changed his name and reentered the ring in 1970, fighting with singular grace and beauty for 25 years.<br /><br />He had four wives, two mistresses and nine kids that ranged from college age to infancy. Kids are one of his great pleasures, his own or any. Ali stops and goes out of his way to pick up a child or ask about people's children. At home, he spends many hours signing Muslim handouts and photos of himself, replying to fan mail, reading the Koran and praying. Islam means to him submitting to the will of God and being at peace. He feels that there is truth in all religions imbued with love.<br /><br />In the '80s, he developed Parkinson's, moving slowly and trembling. The disease is caused, said his doctor in 1987, by injuries sustained in his 61-event boxing career. In the '90s, he lived comfortably on a farm in Michigan with his fourth wife, Lonnie. He travels frequently, usually in the company of his longtime friend and personal photographer, Howard Bingham, for book signing of Bingham's book of photographs, "Muhammad Ali: A Thirty Year Journey." People flock to him, one of the most popular and beloved figures of the sports world of the 20th century. His illness has matured him and made him a serious man, to whom people listen as he slowly formulates the words.<br /><br />Financially, he's comfortable for his later years. In addition to his 200-acre farm in Berrien Springs, MI, Ali owns his Deer Lake training camp and much of the mountain on which it was built - the camp is now being used as a home for abused children - as well as sizable tracts of land in Virginia. He has several vehicles, including a Rolls-Royce and a Winnebago motor home.<br /><br />At the Summer Olympics in Atlanta in 8/1996, he lit the torch, an emotional moment for a nation of fans.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
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<td class="tg-s7xz"><span style="color: white;">Andrew, Prince</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">British royalty, the son of Queen Elizabeth II and Prince Philip, the Duke of York, second in the line of succession to the throne after Prince Charles. Handsome and poised, he gained the nickname of "Randy Andy" for his romantic escapades. On 7/23/1986, he married Sarah Ferguson; they had two daughters together. Andrew and Ferguson separated on 3/19/1992. An official palace announcement of their divorce came on 4/16/1996.</span></td>
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<td class="tg-40k6"><span style="color: white;">Aquino, Corazon</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Filipino aristocracy, from a wealthy family background. She was educated in convent schools and she became the devoted wife of an ambitious journalist and aspiring politician. A homemaker, she enjoyed cooking pasta, playing games with her children and cultivating her garden. Devout, modest, shy and conservative, she has remarked that her happiest times were the three years of exile in Newton, Massachusetts where she lived a simple life outside of the political eye.<br /><br />At the Far Eastern University in 1953, Corozon began dating Benigno Aquino, a wealthy and promising young man. She dropped out of her legal studies after one semester and they married on 10/11/1954, five kids. For the better part of three decades, she lived contentedly in the shadow of her husband.<br /><br />By the early '70s, Aquino seemed a sure bet for the presidency, succeeding Marcos whose final term was ready to expire in 1973. Marcos had different ideas. In 1972 he declared martial law. His first political prisoner was Ninoy Acqino, who remained in prison for more than seven years.<br /><br />Adversity forced Cory out of the house and into worldly matters. She had to get involved in the family sugar business and take over political obligations, becoming her husband's ambassador at large. Their conjugal visits at his prison were nerve-racking. She would carry a large towel and tape to cover the closed circuit TV camera and they whispered because of electronic listening devices.<br /><br />In 1980, Aquino was permitted to go to Boston for heart surgery. For the next three years he had a research fellowship at Harvard. When he returned home on 8/21/1983, he was shot in the head as he left the aircraft. Cory pledged to continue his work.<br /><br />In November 1986, Cory found herself under tremendous pressure to run against Marcos, and with popular support broke the dictatorship to became President. At first her inexperience showed in naïve statements and uninspired public speaking. Gradually she gained strength, fired by the enthusiastic crowds that greeted her everywhere. Cory Aquino has changed history, and history has changed her as well.</span></td>
<td class="tg-40k6"><span style="color: white;">B</span></td>
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<tr>
<td class="tg-8wvm"><span style="color: white;">Arrau, Claudio</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Chilean-American concert pianist, one of the great pianists of the 20th century. In a career that spanned eight decades, Arrau was prized for an aristocratic approach to the great works of the 19th century. He showed his musical abilities early. His dad, Carlos Arrau, died before he was a year old and his mom supported the family by giving music lessons. When he was four, he startled his mom by playing from memory some of the pieces her students were learning. A child prodigy, he gave his first concert at five and began international tours at nine, in 1912. He made his Berlin debut in 1914 and toured Europe in 1918. In 1927, he won the Grand Prix Internationale des Pianistes, in Geneva. He moved to the U.S. in 1941, performing in the U.S. and abroad, winning many international awards. He later resided in Germany, which claimed his mind and his intellect, though his heart always remained loyal to Chile. Arrau had stopped performing in June 1989 after the death of his wife, Ruth Schneider, a German-born mezzo-soprano whom he married in 1937. He was visiting Austria for a rare appearance, a private recital to open a museum when he was stricken with stomach problems. He died 6/09/91 of complications from emergency intestinal surgery, Mürzzuschlag, Austria.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Arroyo, Stephen</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American astrologer and noted author, winner of the 1992 Regulus Award for the Human Experience.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Ashley, Elizabeth</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American actress, young, beautiful and intense when she appeared in her first stage role in "Take Her, She's Mine," 1961-62, for which she won a Tony. In 1963 she starred in the comedy, "Barefoot in the Park," and made her screen debut the following year in "The Carpetbaggers." After two more films, she withdrew from her public life until the early '70s. Once married to George Peppard, 1966-1970, she had one son, Christian, born in 1968. She later married and divorced actor James Farentino. In early 1977, she moved back to Los Angeles from New York City where she had appeared in "Caesar and Cleopatra" with Rex Harrison. Driving to San Francisco to visit friends one weekend, she found herself running out of gas. It was about 3:00 AM without much chance of finding an open station, so when she saw a sign, she turned off the freeway to find an all-night station. While she was checking out the pumps, three men came out of the darkness, very drunk. They beat her and dragged her into the bushes where all three raped her for a nightmare hour, then took her money and left. In pain and raw, she drove off, found a truck stop and an emergency clinic. They cleaned up the wounds but she did not tell them about the rape. It was too ugly, too dirty, too brutal to remember. Ashley managed to forget it. In the next year she gradually put it away so thoroughly that it was not until she testified at the rape trial of a friend that she remembered, 16 years later. After staying with friends for five days, Ashley drove home. She told her nine year old son that she'd had a car accident. Ten months later she sent Christian to stay with his dad and dropped out. She went to St. Bart's, an island in the Caribbean for the next three years, isolating herself. She had an almost irrational attitude of not wanting to be seen as a victim. By 1981, she returned to the States, broke and needing work. She hosted an episode of Saturday Night Live and, from 1982 to 1984, appeared on Broadway and on the road in "Agnes of God." While starring in the Broadway production of "Cat on a Hot Tin Roof," she became friends with Tennessee Williams. On the morning of 3/09/1986, she landed in Edmonton, Alberta, where she and Sandy Dennis were to discuss doing a play together. Customs officials thought her strung out, nervous and red-eyed. They searched her, and after finding cocaine and heroin, took her to jail in Leduc, a small town near Edmonton. Bail was set at $5,000 and she later had to return to court for fine and sentencing. Her autobiography, "Postcards From the Road," was published in 1978. In TV, Ashley played the role of the eccentric Aunt Frieda in "Evening Shade" in the early '90s.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Aurobindo, Sri</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Indian religious leader and writer, a guru. He was well educated with a successful mundane life before he founded his City of Light Ashram in Pondicherri, India. His writings exemplify the highest in Indian thought. "Mother Mira" Richard worked with him in the Ashram and carried on after his death on 12/05/1950, Pondicherry.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Bach, Barbara</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actress, a sensual, voluptuous lead in European and U.S films. A former model, she began in spaghetti-western films and became a Bond girl in "The Spy Who Loved Me" in 1977.<br /><br />She met Ringo Starr on the set of "Caveman," 1981, and they wed the same year. She has done little screen work since. In 1988 they both spent five weeks at an Arizona rehab clinic for alcoholism. She had two kids, Francesca (born 1969) and Gianni (born 1972) from her earlier 10-year marriage to Italian industrialist Augusto Gregorino.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Baldwin, Karen</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American Beauty Queen who was named Miss Universe in 1982.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Balser, Ewald</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">German actor in "Rembrandt," 1942 and "Erotica," 1949. He also directed Shakespeare's "Othello" and Goethe's "Faust." Died on 4/17/1978, Vienna.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Banks, Russell</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American writer who dedicated his sixth novel, "Affliction," to his dad, a pipe fitter who died in 1979. With an alcoholic father, he experienced a childhood of turbulence and confusion. He was the eldest of four kids and was beat up by his dad every once in a while. Despite his home life, he excelled in sports and academics. When he was 12, his dad left the family, leaving a love-hate relationship behind him. Banks became a clerk, and was married and a father at the age of 19. He repeated his dad's pattern of abusive drinking and was divorced in 1960. His second marriage occurred in 1963, lasted until 1977 and produced three daughters. After his divorce, he went back to school, working as a teacher as he wrote. His third marriage lasted for five years, and the fourth was to poet Chase Twichell. "Continental Drift," 1985, was his fifth novel.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Baretti, Pier Cesare</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Italian president of the Soccer Club of Florentina. He died in an airplane accident at Pinerolo on 12/05/1987, 11:38 AM, Pinerolo, Italy.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Beatrice, Princess of York</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British royalty, the first daughter of Sarah Ferguson and Prince Andrew, the Duke and Duchess of York. At the time of her birth, she was fifth in line for the British throne. Her dad was present at her birth, and she weighed six pounds and 12 ounces.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Bellamy, Ralph</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor on radio and TV with more than 400 stage roles and 100 movies. His career spanned eight decades in all, in which he acted with such ease and regal quality that he could do any role. In 1987, he was given an Honorary Oscar.<br /><br />The son of a Chicago advertising executive, he did not care much for scholastics, but did well in the school drama club. At 15, he had a brief job as an extra on a film and it may well have been then that the acting bug bit him. He was expelled from school in his senior year for smoking under the stage, so he worked as a soda jerk, a store clerk and a fruit packer. He ran away from home at 17 and joined a Shakespearean theatre company where he learned to act during the '20s in stock productions. Working as a stage manager, he made $40 a week. Moving on to New York, he found that the big city was not ready for him and reached a point so low that he was living on peanuts, literally, and once stole a bottle of milk from a doorstep.<br /><br />Bellamy continued to work in stock companies while haunting the offices of agents. Finally he won a role. His debut on the New York stage was in "Town Boy," 1929. It closed after two performances, but it led to a good job as leading man with a company in Rochester, playing opposite Helen Hayes. In 1931 he took his talent to Hollywood where he began to make a decent living in films such as "The Secret Six," "Second-Hand Wife" and "Air Mail."<br /><br />During the early '30s, he and Charles Farrell bought 53 acres of Palm Springs land for $3,500 and built their own tennis courts. The property later became the Palm Springs Racquet Club, which Bellamy finally turned over to Farrell. In 1933, he became a founding director of the Screen Actors Guild and throughout his career was active in organizations designed to help actors.<br /><br />His roles began to steadily improve. He returned to New York for stage work at times, co-produced and directed a melodrama and began doing a great deal of radio work. Altogether he had 16 successful years on Broadway.<br /><br />Though he was working steadily, Bellamy was at a low point financially in 1949. A third divorce had hit him hard, along with medical bills for his daughter. It was then he was offered a play, "Detective Story." The play was a hit and led to his award-winning TV series, "Man Against Crime," that ran for five years.<br /><br />"Sunrise at Campobello," in which he appeared as Franklin D. Roosevelt, opened 1/30/1958 and became the triumphant highlight of his professional career. He appeared in several other TV series, "The Eleventh Hour," 1963-64, "The Survivors," 1969, "The Most Deadly Game," 1970 and "Hunter," 1976. His role in "Rosemary's Baby," 1968, was a change of pace, playing a Satanist. In 1983 he was in "Trading Places," and in 1990, in the romantic comedy, "Pretty Woman."<br /><br />His first of four marriages was on 7/06/1941 to 1945. His marriages to Alice Delbridge, Catherine Willard (with whom he had two kids) and Ethel Smith ended in divorce but the fourth, to Alice Murphy in 1949, lasted to his death. His friends remarked that he was always affable and kind. He kept physically fit, exercising at sunrise every morning.<br /><br />Bellamy died of lung illness on 11/29/1991, 2:18 AM PST, Santa Monica, CA.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Benjamine, Elbert</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American astrologer, the founder of the Church of Light who used the pseudonym of C.C. Zain. He is the author of the "Brotherhood of Light" series of philosophical and astrological textbooks. Up until 1900, he studied as a naturalist, at which time he was contacted by the Brothers of Light during a mystical experience. Died in 1951.</span></td>
<td class="tg-htdq"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Berry, Francis</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">English-Malaysian poet and critic who worked in a lawyer's office until his first poem was published in 1934; by 1937 he had won awards. After the war, he lectured on English literature. His first book as a critic came out in 1958, "The Poet's Grammar." He also wrote "Poetry and the Physical Voice," 1962. Married, he had two kids. In 1941, he converted to Catholicism.</span></td>
</tr>
<tr>
<td class="tg-mlny"><span style="color: white;">Biagi, Vittorio </span></td>
<td class="tg-mlny"><span style="color: white;">Fire</span></td>
<td class="tg-mlny" colspan="2"><span style="color: white;">Italian dancer, choreographer and ballet director. He was a member of Milan La Scala from 1958-1960 and the Ballet of the 20th Century from 1961-1966. He appeared in many Bejart ballets.<br /><br />From 1964, he worked in choreography. </span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Binder, Jamie</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American pro astrologer. A successful executive in the communications field with a Masters degree, she quit in 1977 while going through an identity crisis. She devoted her full time to studying astrology and wrote her first book in 1984, which was published by ACS in 2/1989. Her books include "Planets in Work: A Complete Guide to vocational Astrology." A member of NCGR, she has been a consultant since 1979.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Blake, George</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Dutch double agent for nine years, he acted as a spy for England while delivering top secrets to Russia. On 9/01/1948, he was appointed Vice-Consul. Amazingly, he was not arrested as a spy until 4/04/1961. On 10/23/1954, while still a spy, he married. At his trial in 5/1961, he was given a prison sentence of 42 years. Blake escaped his confinement on 10/22/1966 and fled to Russia with the aid of Sean Bourke. The entire escape saga was related in a drama by Bourke entitled "The Springing of George Blake," 1970.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Bone, Jan</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American freelance writer who sold over 400 articles to the National Enquirer alone, plus many more to other magazines and papers. Her books include "Understanding The Film," 1976 and "The Thompson Indictment," an expose of political corruption, 1978. She was married in 1951 and has four sons.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Borbon, Princess Elena</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Spanish royalty, the first daughter of Juan Carlos and Sophia. She married Jaime de Marichalar on 3/18/1995 in Seville in front of 1,300 guests. The 110,000 citizens of the city celebrated the marriage for three days. Borbon and Marichalar met in 1987 while attending the Sorbonne; they courted discreetly and married extravagantly. As the Duke and Duchess of Lugo, they moved to Paris.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Bordet, Jules</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Belgian scientist, a bacteriologist and physiologist who was awarded the Nobel Prize in 1919.<br /><br />Died on 4/06/1961, Brussels, Belgium.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Brenner, Paul</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American physician, an obstetrician and leader in the holistic health movement.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Brewster, David</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Scottish scientist, a famous Victorian who invented various optical instruments and the kaleidoscope while working in the fields of reflection, absorption and polarization of light. A prodigy, he entered the university at 12 to study for the ministry. By the time Brewster completed his studies, he had settled on science as his field. During his distinguished career he received many honors, including knighthood. Died on 2/10/1868.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Bridges, Tom</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American astrologer whose interest began in 1984 after three years study. He worked three years for Llewellyn, then four years for Matrix where he co-developed their computer programs on horary and midpoints. Bridges wrote the synastry text for Philips Intermedia. In 8/1994, he began with "Mountain Astrologer." Bridges is the teacher of an eight-part astrology course at Cheshire Rose Books, Sacramento called "Expanding Astrology Techniques." He was married to Randy, a realtor, on 3/05/1988.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Brynner, Yul</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Russian-American actor who was dynamic, slightly mysterious and famous for his shaven head and piercing gaze. The son of a Mongolian mining engineer and a gypsy mother who died at his birth, he spent his first eight years in China. He was then sent to live with his maternal grandmother in Paris, but she died soon after. He attended school in Paris for a while but dropped out at 13 to join the circus, performing as an acrobat and clown. After an injury on the high trapeze, he turned to the stage. An early bout with TB also limited his gymnastic activities, so he moved into the performance of Russian and Gypsy songs in clubs. He learned English to go along with his ability to speak Russian, French, Japanese and Hungarian.<br /><br />In 1941, Brynner moved to the U.S. His New York stage debut was in February 1946 on Broadway, playing opposite Mary Martin in "Lute Song." After 142 performances, Brynner took the show on tour. In 1948 he returned to New York, settling into the role of actor, director and producer in the fledgling TV industry, ultimately directing episodes of "Studio One," one of the more successful live anthology shows of the '50s. A knowledgeable photographer, he directed TV from 1946-1947.<br /><br />He fell in love with the script of "The King and I" when Richard Rodgers and Oscar Hammerstein offered him the role. The opening in New Haven, CT, February 1951, was a disaster. The show was nearly five hours long and had only conflict between the King and Anna, without the tenderness and attraction that was added later to the script. With the book cut and sweetened, they opened in New York on 3/29/1951. It was a first-night hit. Brynner won a Tony in 1952 and an Oscar for the 1956 movie version.<br /><br />A non-conformist, he was one of a kind and unique. It was for his audition for "The King And I" that he first shaved his head. His first starring movie was "The 10 Commandments." The films "Anastasia," "The King And I" and "Commandments" were all done in an 18-month period. For the film version of "The King And I," he repeated his charismatic stage performance.<br /><br />Brynner resumed his role as the King of Siam on 5/03/1977 until the end of his life, with a last performance on 6/30/1979, reaching a total of 4,625 times that he had played the role in 26 years.<br /><br />Brynner made a second marriage in 1960; their one daughter, Victoria, was born in their home in Switzerland in 1962. During his third marriage, he adopted two Asian girls. His fourth wife, Kathy Lee, was an Asian dancer in the show.<br /><br />A five-pack a day smoker, he was diagnosed with lung cancer in 1983 and given three months to live. He underwent radiation treatment in Hanover, Germany. After spending two months in a clinic for treatment that included a controversial vitamin A-based diet of spinach, carrot juice, green leafy vegetables, pineapple juice extracts and chemicals, he declared that he was cured.<br /><br />A fighter to the end, he died on 10/10/1985, 1:00 AM, New York.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Buchan, Sir John</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Scottish politician and novelist who published more than 50 books.<br /><br />He was elected Chancellor of Edinburgh University in 1937.<br /><br />Died on 2/11/1940, Montreal, PQ, Canada.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Butler, Dollie Lee</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American lawyer and lecturer who was one of the founding members, and the attorney, for Far Horizons Theosophical Camp in the Sequoia National Forest.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Byron, Ada</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British noted family, the Countess of Lovelace. She is the daughter and only legitimate child of the sixth Lord Byron, whose marriage to her mom lasted a year. Her mom was obsessed with dominating and controlling her, giving her a good education, but massive social repression. Studied from age five, she showed an early gift in math, and gradually formed an ambition to work as a mathematician. Byron was an accomplished harpist. With few friends, she married an older man at 19 and had three kids before she was 24. On 6/05/1833, she met Cambridge professor Charles Babbage at a party. As they became friends, she lost interest in her household and social life, offering to work as his assistant in 1842. Byron did a brilliant job with technical annotations to his calculator. Historically, her genius is recognized, and she is often called "the first programmer. "In 1841, she was greatly upset by the expose of a family scandal, which alleged that her dad had an incestuous relationship with her half-sister. Byron had health problems and mood swings that ranged from elation to fatalism, which she treated with opium and brandy. She also had an impulsive love affair. Found to have uterine cancer, Byron died just before her 37th birthday on 11/28/1852.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Cage, Nicolas</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor and noted family, the son of August Coppola, a professor of comparative literature and dancer Joy Vogelsang. He was born with that certain something that the camera captures, that invisible magic that makes him impossible to ignore, that makes him hauntingly memorable. From the beginning of his career he was described as a "punk hunk," with "endearingly dopey sexuality."<br /><br />The youngest of three sons, he was six when his mom began having mental health problems with which she spent years at a time in institutional therapy. He was 12 when his folks divorced and he went to live with his uncle Francis in northern California. Angry and hitter, a hyper kid, he was always the weirdo, the kid who was not picked to be on the team. "I had a lot of difficulty making sense out of life," he said. By 15 he was acting in local theater and TV roles, usually playing punk and crazy guys, turbulent, outsider roles. He gained a reputation in the '80s as wild and weird, going through his problem period with drugs and alcohol and one-night stands.<br /><br />In film, he played in "Raising Arizona," "Firebirds," "Wild at Heart," and "Moonstruck," 1987, in which he made a memorable impact. On 3/25/1996 he was nominated for an Oscar as Best Actor for "Leaving Las Vegas." His sixth movie in two years, "Snake Eyes," opened in August 1998.<br /><br />Cage broke up with his girlfriend of the prior four years, Jenny Wright, in 1987. He and his girlfriend, actress Christina Fulton had a son for whom they share custody, Weston, born on 12/26/1990, Los Angeles. After eight years friendship with actress Patricia Arquette, they married 4/27/1995. They had first met in 1987 and at that time, went together for three weeks before their scene faded. Over the years they kept in touch while each had a child with someone else. Neither being conventional, they bought a castle in Hollywood as their home.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Canoletti, Grace</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Brazilian model who was fourth born of eight girls. She was a redhead who worked in TV ads from 1981. She was the only girl not born in Sao Paulo, born at the home of her maternal granddad.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Capodaglio, Wanda</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Italian actress and comedienne.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Carpenter, Richard</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American musician, a member of a popular brother-sister singing team, "The Carpenters" who sold millions of hit records in the early '70s. He started piano at 12 and studied classical piano at Yale before the family relocated to Downey, CA, 1963. He formed his first group in 1965; a jazz-pop instrumental trio with sister Karen on drums and their friend Wes Jacobs (who later took a seat in the Detroit Symphony) on bass and tuba. They won a Battle-of-the-Bands at Hollywood Bowl and landed a contract with RCA. The two singles that they cut were considered "too soft" and never released. The trio broke up in late 1966.<br /><br />The Carpenter siblings recruited four Cal-State students into the vocal harmony band "Spectrum," playing local gigs. As "The Carpenters" they hit the charts by 1971, moving into Emmy country. They hosted a short-lived variety series on NBC in 1971, and among their credits, played the White House by the request of President Nixon 5/01/1974.<br /><br />On 2/04/1983, Karen Carpenter died of complications from anorexia at their parents home in Downey, CA, leaving Richard solo.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Carroll, Lewis</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">English logician and mathematician who was a shy, fussy bachelor. Regarded as a crank, he stammered badly and was deaf in one ear. However, Carroll liked little girls, and, for the daughter of a friend, began to create fantasy story. He authored fables and fantasies, including "Alice in Wonderland," 1865.<br /><br />Died on 1/14/1898, 2:30 PM, Guidford, England.</span></td>
<td class="tg-40k6"><span style="color: white;">B</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Clayton, Derek</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British track and field star, the world's fastest marathoner 12/03/1967 when he stunned the athletic world by becoming the first to race the classic distance in two hours and 12 minutes, a title he held to 10/25/1981 when the record was beaten by a 23-year-old American, Alberto Salazar.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Close, Glenn</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American actress, the daughter of a surgeon and a 12th generation New Englander raised on the family 500-acre estate. She performed in high school plays and folk-singing groups, though actually a lyric soprano, continuing to polish her craft through college before hitting the New York stage. She made a film debut in 1982, "The World According to Garp." A natural actress, Close won nominations as Best Actress in "Fatal Attraction," 1987 and "Dangerous Liaisons," 1988. Her top roles also included "The Big Chill" and "The Natural." On Broadway, she won a Tony for "The Real Thing," and also raves for her "Sunset Blvd." Close lives in New York as a single mom to her daughter Annie Maud, born in 1988 with producer John Starke. With two marriages behind her, she announced her engagement to eight-year-younger stage carpenter Steve Beers in March 1995.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Cole-Whittaker, Terry</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American Religious Science pastor from 1977, a fireball who took San Diego by storm with her up-beat, you-can-do-it message. A former beauty contest winner as Miss California in 1968, she became a housewife and mother of two daughters when she made the first of her four marriages. She is the author of "How to Have More in a Have Not World."</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Collins, Gary</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor, a feature player in minor films that include "The Pigeon that took Rome," "Airport," and "Angel in my Pocket." He later was the TV host of "Hour Magazine." Collins married a former Miss America, Mary Ann Mobley.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Collins, Kevin Andrew</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American kidnapped child. On 2/10/1984, age 10, he was abducted, San Francisco, CA. His parents founded the Kevin Collins Foundation to help other parents who 've had their kids stolen, by putting out flyers, organizing searches and forming support groups. Kevin was never found.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Cortes, Armand</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American character actor on screen and stage from 1914. His films include "The Return of Tarzan," 1920, "The Crowded Hour," 1925 and "Bluebeard's Eight Wife," 1938.<br /><br />Cortes died 11/19/1948, San Francisco</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Currie, Edwina</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British conservative politician and Jr. Minister in the Dept. of Health and Social Security. Returned at General election 6/11/1987 as a M.P.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Dahl, Arlene</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American actress on film and TV whose works include "The Black Book," 1949 and "Journey to the Center of the Earth," 1960. She had four years on a TV soap, "One Life to Live." She later became a cosmetics businesswoman. After writing 16 health and beauty books, she published her first novel in 1987, "The Corporate Body." A great beauty, Dahl married seven times, the last to 18-year-younger Mark Rosen. She accepts the theory of reincarnation and avidly follows astrology, becoming a practicing pro herself.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Daly, Tyne</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American actress who drifted into her field with stage work, low-budget films and TV guest shots as a natural outcome of having acting parents. Her career began with traditional roles, type-casting her in "modern woman" shows with a message, often feminine or other vital issues. In the early '70s she began to guest in a wider range and became a superstar with the popular TV series "Cagney and Lacey"; playing Cagney, one of two female cops. Daly married Georg Sanford Brown; three daughters born in 1968, 1971 and 1985. He husband directed some of the episodes and played in a few. After C&L concluded in 1988, Daly packed on 40 pounds which did not hamper her talent; she won a Tony for "Gypsy" 1990. Her credits also include an Emmy nomination in 1977 for "Intimate Strangers." She divorced her longtime husband with a bitter custody battle for their youngest daughter, Alexandra. In 1996 she was pictured socially with Clarence Williams, a black actor formerly on Mod Squad.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Dandridge, Dorothy</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American entertainer and actress, accomplished as a singer and actress on stage, film and TV. The daughter of actress Ruby Dandridge, she and her sister appeared together as youngsters. She played in the Cotton Club, 1938, Las Vegas, New York Mocambo, 1951, Rio de Janeiro, 1953, and Palm Springs, 1963. Her films from a debut in 1937 included "Since You Went Away," 1944, "Island in the Sun," 1957, "Porgy and Bess," 1959 and "Malaga," 1962. On radio, she played in a series, "Beulah." Dandridge married and divorced dancer Harold Nicholas. She published her autobiography in 1970, "Everything and Nothing." Died 9/08/1965, West Hollywood, CA.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Depp, Johnny</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor, a baby-faced heart throb who began as a guitar player with the "Rock City Angels" when he was cast in the TV series "21 Jump Street" in 1987 to become a star. His screen debut was in "Nightmare on Elm Street" followed by "Cry-Baby" and "Edward Scissorhand."<br /><br />Depp has a kind and generous side, but for the most part shows off his wild temper, a dark side that is self-destructive with stupid thrill-seeking tricks such as blowing on fire with a mouth full of gas. He lives a vagabond life, spending a lot of time at the Viper Room, the club he owns in Hollywood. He started smoking at age 12 and now chain-smokes. He lost his virginity at 13 and was using all types of drugs by 14. He married at 20 for two years.<br /><br />On 9/13/94, 5:30 AM, Depp was arrested for criminal mischief, suspected of a drunken fight with his girlfriend, model Kate Moss, during which he wrecked a $1200 per night room in a posh New York hotel resulting in $10,000 in damages. Randi Reisfeld has published a biography on Johnny Depp.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Dern, Laura</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American actress and noted family, the daughter of Diane Ladd and Bruce Dern, both Oscar-nominated actors, and related on her mother's side to playwright Tennessee Williams. Her parents divorced when she was two and she grew up with her mom. She was 12 before she formed a relationship with her dad. By nine, she was interested in acting. Though not encouraged by her parents, Dern made a film debut as an extra in "Alice Doesn't Live Here Anymore." She took acting classes and had a first substantive role in "Foxes" at 11, and a breakthrough as a blind girl in "Mask." Playing opposite her mom in "Rambling Rose," they both earned Oscar nominations. In 1993 she played in the monster hit, "Jurassic Park." She and her co-star, Jeff Goldburg, began a romance at that time. By 1997 they were no longer together and she was seen in the company of Billy Bob Thornton. Dern studies metaphysics and philosophy, practices yoga and meditation.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Diepenbrock, Alphons</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French composer of the romantic movement; he wrote masses and church music. Largely self-taught, he was a music teacher. Died 4/05/21, Amsterdam, Netherlands.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Dudley, Robert</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">British nobility, the fifth son of John Dudley. When Queen Elizabeth I ascended the throne, he became her favorite with offices, honors and wealth bestowed upon him. In 1564 he was created Baron Denbigh, Earl of Leicester and Chancellor of Oxford University.<br /><br />In his expeditions, he demonstrated no military capacity. Due to his close friendship with the Queen, when his wife, May Robsart, was found dead at the foot of the palace stairs, he was suspected of aiding her fall. He later made a second marriage and had a son 8/07/1574. He denied the marriage but did agree to support the boy.<br /><br />Died 9/04/1588 at Cornbury, England.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Duel, Peter</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American actor; star of TV series "Alias Smith And Jones". He discovered acting while in college. A heavy drinker, he also dealt with emotional problems. He had a car accident on 10/24/1970 while intoxicated. He was beginning to receive praise for his series, but was discontented with it. Nonetheless, it was a shock when he committed suicide by gunshot in his mouth 12/31/1971, 1:33 AM, PST, Hollywood, CA.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Duncan, Sandy</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American actress, on-screen after her appeal in TV commercials caught the attention of the public. Her films include "Star Spangled Girl," 1971. She made her bid for stardom in two short-lived TV series, and replaced Valerie Harper in "The Hogan Family," 1987-1991. She lost one eye in a serious operation to remove a brain tumor.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Eco, Umberto</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Italian novelist whose "Name of the Rose," 1980, was made into a 1986 film. His 1988 novel, "Foucault's Pendulum," involves occult themes and conspiracies. A medieval scholar for more than 30 years, his only claim to popular fame was a chatty weekly column in Italian newspapers until his phenomenal overnight success in early 1980. He also publishes essays, a resident of Milan, Italy.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Fairchild, Morgan</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actress best known for good underwear and bad intentions in seductive roles in various TV series, "Search for Tomorrow," 1971, "Dallas," 1978, "Flamingo Road," 1981-1982, "Paper Dolls," 1984, "Falcon Crest," 1985-1986 and "The Haunting of Sarah Hardy," 1989. Though she made a few films, TV was definitely her medium.<br /><br />Shy as a kid, her mom put her in acting school. She married at 17 and divorced. She went through a prima-donna period while she was on "Flamingo Road," flouncing her weight around.<br /><br />She published a book "Superlooks" 1984. In the early '90s she had a breast enhancement that was poorly done and looked like two grapefruit stuck on her chest. When the job was redone later it was much more attractive.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Ferguson, John Errol</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American homicide; found guilty on 5/25/1978 of six murders and sentenced to death by execution. By 1990, he was still on death row with delays caused by appeals. A good-looking black guy, he was diagnosed as homicidal and dangerous by court psychiatrists in 1975 when he was acquitted of six robberies and two assault charges on a plea of insanity. He was given 18 months prison and two years probation and released in May 1977. That same month, he robbed, savagely beat and shot an elderly couple in a motel. On 7/27/1977, he forced his way into a private home posing as a repair man and with three accomplices, shooting eight people in the head execution style, six of whom died. It was a drug-related crime. Ferguson was suspected of rapes on October 14 and October 30, 1977. On the later date, he shot two teenagers parked in a car and wounded, they drove off. He raped a woman on October 31. On 1/08/1978, he shot to death two teens in a parked car. He was arrested 4/05/1978 and taken to trial.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Fitzgerald, Zelda</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American noted family, the wife of F. Scott Fitzgerald. Slender, with bobbed hair and short dresses, she was the epitome of the Jazz Age. She married Scott in 4/1920, and they drank and played together. Their one daughter was born in 1921, and she had several abortions. Slipping into dementia from 1925, she first entered a Swiss sanitarium in 1930. In and out of sanitariums, during her lucid periods she studied ballet, wrote and painted. She died in a hospital fire 3/10/1948, Asheville, NC.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Flight Manager</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"> <span style="color: white;">Scottish-American Flight Manager for a 27-year career, retiring in 1953. He moved to Canada at 19, in 1953. He married and divorced, had a couple of children. After retirement, he and his companion, Dawn, opened a Bed-and-Breakfast home.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Friedman, Stanton</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American nuclear physicist and propulsion systems expert who worked on the Pioneer Spacecraft. Known as "Mr. Flying Saucer," he has made a study of saucers since 1959 and is convinced that 90% of all sightings are explainable and that at least 30,000 of them are valid phenomena. A UFO advocate, he began lecturing to large audiences in the United States and Canada in 1968 and has given over 400 lectures.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Gandhi, Sonia</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Italian-Indian political wife. The daughter of an industrialist in Turin, straightforward, intelligent and something of an introvert, she met Rajiv Gandhi when they were both students at Cambridge University. It was love at first sight and they married on 2/25/68 in New Delhi. Their son Rahul was born in 1971 and daughter Priyanka in 1972.<br /><br />Sonia was reared in a rigidly traditional household in a small industrial town in northern Italy. She and her two sisters were not allowed to date boys unchaperoned. Yet, when she was 18, she was allowed to go to a language school in Cambridge. In January 1965, she met 20-year-old Rajiv while having lunch with a friend. In spite of their language barrier, their attraction was mutual, intense and permanent. A friend described their relationship as "an overwhelming love story" up to the time of Rajiv's death. After they married, Sonia moved to the family home in New Delhi where the different generations lived and ate their meals together. Sonia was content to play the role of the faithful daughter-in-law, the "bahu," running the household, buying clothes for Indira and putting up with Sanjay's temper tantrums. Though her mother-in-law, Indira Gandhi, did not approve of her son marrying an Italian, they later became close. Sonia became an Indian citizen on 10/28/1983, giving up her Italian citizenship. Articulate in six languages, she became adept at grass-roots campaigns, feeling that the Indians were her family.<br /><br />Though the household was dominated by politics, Rajiv and Sonia led an apolitical life and avoided the more glamorous end of New Delhi society. Rajiv worked as a pilot for the notoriously incompetent Indian Airlines, where he became known as a stickler for efficiency. When Sanjay died in an air crash in 1980, Rajiv reluctantly had the family destiny thrust upon him though Sonia fought like a tigress to dissuade him from entering politics.<br /><br />When Indira Gandhi was assassinated on 10/31/1984, Rajiv stepped immediately into her shoes as P.M. As the new P.M., Rajiv was optimistic, though utterly unqualified for the job. After Indira Gandhi died on 10/31/1984, it took Sonia literally years to come to terms with the horror of the assassination. She avoided seeing people and often fell silent for long periods. Taking up art restoration as a hobby, she edited the correspondence between Indira and Nehru in two volumes. On 5/21/1991, suddenly and violently, her husband was assassinated. Sonia was offered the post of Party President within 24 hours of her husband's death but she refused due to her dislike of publicity or the limelight and her fear of exposing her family to further risks.<br /><br />She retreated into herself, drawing consolation from her children and her home, which became a shrine to her beloved martyred husband. Her circle became small and closed and she made few public appearances. Her private secretary, Vincent George, became her spokesman. In 1997 she quietly became a member of the Congress Party. Her position is aided by the fact that she looks much like the Nehrus, who are high-caste North Indians, with her dark hair and brown skin. After her husband's death she dedicated her life to raising her son, now 27, and daughter, 26, and to running foundations.<br /><br />She finally agreed to enter politics when party leaders assured her that a "working" president of her choice would take care of day-to-day party work.<br /><br />The election was like no other country had ever seen. There were more than 600 million registered voters and the ballot boxes had to be transported by donkey, fishing boat and mountain porter. There were nearly 5,000 candidates, some of whom were colorful, if unlikely, such as a bandit queen who had 63 court cases pending against her. Anarchic violence exploded in voting disputes. Some of the voting boxes were captured by bandits who shot the guards and stuffed the ballet boxes. India has over a thousand different languages and entrenched religious and caste divisions, and many powerful splinter groups have broken off into chaotic segments.<br /><br />On 1/11/1998 Sonia Gandhi emerged from her private life to campaign on behalf of Congress, giving her first speech in Sriperumbudur, where her husband had been murdered. She told the crowd, "Devotion to India brings me before you, not a desire for political office." She covered the subcontinent by jet and helicopter, visiting 138 constituencies in a 34-day tour, an unparalleled campaign. She drew larger crowds than any of her rivals. At a rally in Old Delhi, some 80,000 people merged, screaming and pressing forward when she appeared. She scurried to the front of the platform like her late mother-in-law, mouth set tightly, no time to waste, with her two handsome, smiling children following her. She read her speech in a woeful voice with heavily accented Hindi, telling the story of her life; how she had taken the bullet-ridden body of her mother-in-law to the hospital through the streets of Delhi and how she had sacrificed her husband for India. She told how she had arrived from Italy in 1968 with a return ticket, but "Delhi was the place of my second birth and the ticket, like my past, was lost in the sands of time." People wept, and when she repeated "Hail India" three times, as Indira Gandhi had once done, the crowd roared.<br /><br />On 3/14/1998 Sonia Gandhi was elected president of India's Congress Party, defying Indians who had said that she was not fit to head the organization that led India to Independence 50 years before. Her election reaffirmed the family dynasty that has dominated the party since the days of Jawaharlal Nehru, India's first post-independence Prime Minister.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Gavazzeni, Giandrea</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Italian musician, conductor, composer and critic.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Gelfan, Corinne</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actress and folk singer since 1966, with credits in many theatrical productions, commercials, and musicals, including musical comedy. She did six episodes of "General Hospital" in 1984.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Genovese, Vito</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Italian-American Mafia chief since 1957, known for being in the rackets and the business of murder. "Don Vitone" as he was called, reportedly directed operations from prison while serving a sentence of 15 years. He was married; two kids. Died in Leavenworth, KY prison of a heart attack 2/13/1969.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">George V, King</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">British royalty, the second son of Edward VII and Princess Alexandra and heir to the throne when his brother, the demented Prince Albert Victor, died in 1892. He was trained for the Navy and became Vice-Admiral in 1903. Succeeding his father in 1910, he gained immediate and lasting popularity for his courage and national devotion during WW II. He married Princess Mary of Teck in 1893; six kids; five sons and a daughter.<br /><br />The story endures that when he suffered from terminal illness at age 70, his doctors gave him a merciful overdose of morphine with the agreement of his family, 1/20/1936, 11:55 PM, Sandringham, London.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Giscard d'Estaing, Valery</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French financier and politician, the President of France 5/19/1974 succeeding Georges Pompidous. He served with the French Resistance during Nazi occupation during WW II and began his government career specializing in finance, 1952. Wealthy, aristocratic, intellectual, he skis, hunts, plays football and flies his own plane. Married; four kids.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Goria, Alexandre Adolphe</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French composer and chamber pianist, noted in the 19th century.<br /><br />Died 7/06/1860, Paris.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Gortner, Marjoe</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American youthful evangelist who, from the time he was an adolescent, toured and preached the Bible Belt for 15 years. He became an actor in 1971, playing himself in the film "Marjoe." His role in "Marjoe" was followed by B films and minor TV roles. Gornter produced "When You Comin' Back, Red Ryder?" in 1978.<br /><br />He was married at age 16 and had one daughter. Gortner married Candy Clark in 1978; the relationship lasted for only a year.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Gough, Melvin N.</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American pilot; graduated as a Navy pilot from Pennsacola in the '20s to become a famous test pilot and chief of the Flight Research Division of NASA 1959.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Griffith, D.W.</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American stage actor and road manager before entering film, when he became a pioneer director and producer in blossoming Hollywood. He produced the first full-length feature in 1915, "Birth of a Nation." Died of cardiac arrest 7/23/1948, Hollywood, CA.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Hamilton, Scott</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Canadian ice skater, a superlative Olympic figure skater who won the U.S. Men's Championship in 1981 and 1982 and the World Championship in 1981 and 1982. Symbolizing eternal youth in skating with his charismatic energy and gnome-like and puckish features, he appears wispy and fragile at 5'3", 115 lbs. just seconds before blowing audiences away with his superlative skating; he is tremendously exciting in the arena.<br /><br />Adopted as an infant by Ernie and Dorothy Hamilton, he suffered from digestion problems up until age nine. It was then that he took up skating, with his wins starting in 1981 with four consecutive national and world titles to go with his Olympic medal. His mom died of breast cancer in 1977.<br /><br />Since 2/1997 he has suffered from back and stomach pains. On 3/16 he went to the doctor to find that he had testicular cancer that had spread to the abdomen. As he is a beloved big brother to other skaters, his colleagues rallied around him through the next three months of chemotherapy treatments.<br /><br />On 6/24/1997, he had surgery to remove a cancerous growth on his abdomen in Cleveland, OH. His diagnosis remained positive, and was expected to return to the ice in September.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Hansberry, Loraine</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American writer of a production that was the first play by a black woman to be produced on Broadway, running for 19 months. "A Raison in the Sun" was a wonderful caustic comedy of a black family in Chicago that received a windfall of money.<br /><br />Hansberry was married on 6/20/1953.<br /><br />Her second Broadway play, "The Sign in Sidney Brustein's Window," 10/1964, was produced three months before she died of cancer on 1/12/1965, New York, NY.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Hauer, Rutger</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Dutch actor who does well in villainous roles such as in "Blade Runner," "Nighthawks," and "The Hitcher." From his first film, "Turkish Delight," 1973, he spent 18 years honing his craft with powerful portrayals of androids, terrorists, Nazis and psychopaths, with the occasional role of a heroic figure.<br /><br />The son of acting parents, he ran away to sea at 16 for a year and spent a short time in the Dutch army before entering drama school and graduating in 1967.<br /><br />World known and traveled, Hauer lived in Ireland with his lady love of 16 years; they married in 1986.<br /><br />A decade later he had homes in northern Holland and in Hollywood where he spends two-thirds of his time in film production. From 1978, he has worked almost exclusively in American productions.<br /><br />He has had a vasectomy as a precaution against pregnancy with his lady.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Hayes, Woody</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American football coach at Ohio State University in 1951 who went to the Rosebowl eight times. With his leadership, Ohio State dominated the big ten in the mid-'70s; he won four years in a row, 1973-76. However, Hayes found it very difficult to adapt to the updated game methods of modern athletes. He reached the end of his career when he punched a Clemson player on national TV during the Fiesta Bowl; he was fired shortly after.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Herold-Paquis, Jean</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French journalist who collaborated with the Nazi's.<br /><br />He was executed for treason on 10/11/1945 at Montrouge, France.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Hershensohn, Bruce</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American broadcaster, media commentator and author who was the one time head of the U.S. Information Agency's film division. He is the author of "Gods Of Antenna," and has held a lifetime interest for politics. The highly intelligent son of a physician, he became a TV commentator in 1977, capturing huge ratings. He later became a political critic on the news, adding radio commentary in January 1980.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Hussein, Prince</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Jordanian royal family, he is the Prince of Jordan and the son of King Hussein and his second wife, Toni Gardiner.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Johnson, Kevin</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American professional athlete of basketball and baseball. Selected by the Oakland A's in 1986 as a free agent baseball player, he then started playing basketball for the Phoenix Suns as a first round draft pick in 1987.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Juliana, Queen</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Dutch Queen of Holland 09/06/1948 upon abdication of her mother, Queen Wilhelmina, due to her mother's poor health. She had been a member of the Council of State for 20 years and was considered the mother of the country. Unpretentious, her countrymen considered her one of them. During the WW II occupation, the Queen and family resided in Canada for a five year stay.<br /><br />Queen Julianna was the only child of Queen Wilhelmina and Prince Consort Henry. Queen Juliana met Prince Bernhard in 1937 and they had four daughters together, 1938, 1939, 1942 and 1946.<br /><br />This continued three generations without any male heirs.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Junger, Sebastian</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American writer, the author of a best-selling first novel, "The Perfect Storm," 1997, the story of the 1991 sinking of a Gloucester, MA fishing boat. The book tells the story of the six men who went down with the Andrea Gail in one of the worst storms on record, a three-day northeaster that slammed ashore on 10/31/1991. Junger has built his writing credits with articles for magazines on such topics as wilderness wildfires, nature and its awesome capacity.<br /><br />The son of a physicist and an artist, Junger forged his own path, enjoying the solitude of the woods and of the challenges of survival. He made extra cash as a high-climbing tree cutter, a hard and dangerous job that gave him with a chain-saw gash in 1994. He graduated from Wesleyan University with a degree in cultural anthropology in 1984, drifting into odd jobs as he honed his writing.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Kaufman, Andy</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor who performed his off-beat, highly original, stand-up comedy and impressionist routine on TV, in clubs and concerts. His act ranged from brilliant to boring to bizarre. His career snowballed after he began appearing on Saturday Night Live, 1975, and then became a regular on the series, "Taxi," 1978. He was in the film "Heartbleeps" with co-star Bernadette Peters, in which he played a romantic robot.<br /><br />He died of lung cancer 6/16/1984 at the age of 35.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Keppler, Wilhelm Carl</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">German personal advisor, engineer, chief liaison and industrialist, he was Hitler's personal advisor on economic affairs and the chief liaison between the Nazi party and the business world.<br /><br />On March 5, 1933 he was elected to the Reichstag and appointed Reich Commissioner for Economic Affairs. During WW II, he served as Secretary of State. At the end of the war, he was sentenced to ten years prison in the trial of April 14, 1949.<br /><br />Released by clemency action on 2/1/1951, he died June 13, 1960</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Kirkland, Gelsey</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actress, dancer and prima ballerina. After seven years of study, at the age of 15, she worked at the Corps de Ballet of NY, two years later a soloist and a prima ballerina for both the NYC Ballet and American ballet.<br /><br />A daily cocaine user by 1986, she met writer Greg Lawrence and together they broke the coke habit. She didn't dance for two years. She was so browbeaten by Ballentine that she went through cosmetic surgery (shorter ear lobes, silicone injection of lips and breasts) to make herself perfect.<br /><br />By 1994 she was teaching dance in Manhattan, with an acting debut to her credit in a role on L.A. Law 2/10/1994.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Knight, Jordan</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American musician and member of "New Kids on the Block," a manufactured rock group of superstars that originated in the working class of Boston. They were discovered by a promoter who hooked up with Motown to hype the act, composed of the two Knight brother, McIntyre, Wood and Wahlberg.<br /><br />Jordan is the lead singer and known as a hunk to his screaming teenage fans.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Legros, George Cardinal</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American writer, poet, teacher and astrologer. The editor of "Fate's Astrology Forecast" in the early '60s, his book of poems "The Mystic Testament" was published in 1961 and he was the publisher of the "Messiah" until his death. Died of lung failure 2/15/1988 Weaubleau, MO.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Lightfoot, Leonard</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American actor, portraying the role of the lawyer in the TV sitcom "Silver Spoons."</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Lilly, Antonietta</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American artist, author and psychotherapist. She co-authored the book "The Dyadic Cyclone" and was a contributor to the book "Communication Between Man and Dolphin" with her husband, John Lilly.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Lindemann, Ricardo</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Brazilian astrologer, interested in karmic and spiritual counseling, He was the Vice-President for the Theosophical Society of Latin America.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Lindfors, Viveca</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Swedish actress and director with a face carved of magnificent planes and angles. She debuted in film in 1940 and moved to Hollywood in 1946.<br /><br />Lindfors had three marriages and three children. She died 10/25/1995.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Long, Howie</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American football linemen, actor and TV sports commentator. Playing for the Raiders for 13 years, he was one of the best defensive linemen the NFL has ever produced. Winning a Super Bowl Ring in 1984, he was also known for misdeeds and fighting on the field. Starring in nine Pro-Bowls, numerous trophies and awards, sustaining nine surgeries, he retired in 1994. He then became a TV commentator for Fox-Sports for two years leading him into two titled acting films, "Broken Arrow" and "Firestorm" in 1997. Long is also the Chairman of Athletes and Entertainers for Kids. Raised in a tough section of Boston, his father was a milk loader and his mother was a homemaker. His parents splitting up when he was twelve, he lived with his maternal grandmother and other kin. At age 14, he was playing football in school. He married Diane Addonizio in 1982; three sons; a family he neglected due to putting a career he loved in first place.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Long, Huey P.</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American politician known as "The Dictator of Louisiana" while he was Governor, 1928-1931; lecherous and corrupt, nonetheless a beloved and popular man. He resigned to become a US Senator 1931-1935. While walking down a State Capitol corridor 9/07/1935 he was shot. He died three days later, 9/10/1935, Baton Rouge, LA.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Luther, Martin</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">German reformationist who was ordained a Roman Catholic priest in 1507, but broke from the church in 1519, denying Papal supreme power. Condemned as a heretic, he began the Reformed Church in April of 1525.Luther married in 1525, enjoying a happy home life with six kids. Died on 2/18/1546 Eisleben, Germany.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Maffei, Michele</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Belgian swordsman who was a Gold Medal winner at the 1972 Olympics in Monaco.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Magritte, René</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Belgian painter who was among the greatest creators of poetic images while remaining at the same time consistently realistic. He started as a modernist but became one of the surrealist group with the belief that through ideas and conscious manner one became adept. Prior to devoting himself to art, he worked as a civil servant. His childhood was heavily traumatic with the death of his mother when he was 12; she drowned herself with no explanation. In 1913, Magritte met his wife-to-be for the first time. The couple drifted apart, but eventually re-met in the early '20s and married. In 1927, they moved to Paris but three years later returned to Brussels where they spent the rest of their lives. Died on 8/15/1967, Brussels, Belgium</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Mair, Michael</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Italian skier who specializes in downhill racing.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Mans, Keith</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British politician, a Member of Parliament returned at the general election held on 6/11/1987.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Marx, Jenny Julia</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">British activist, the fourth daughter and sixth child of Karl and Jenny Marx in their 12 year marriage, the only one to unite her lot with England and marry an Englishman. From 1883 she played a significant part in the British working-class movement.<br /><br />Known as "Tussy" she committed suicide at a youthful 43, in 1898.</span></td>
<td class="tg-40k6"><span style="color: white;">B</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Masina, Giulietta</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Italian actress who acted with such depth and passion that she was able to imbue the ordinary with touches of the bizarre. Some of her films included "La Strada," "Juliet of the Spirits," and "The Madwoman of Chaillot." Her screen debut came in Rossellini's "Paisa," and she was the star of several films written by her husband in the '50s and '60s. She married Federico Fellini, the great director, on 10/30/1943. They first met in 1942 when Masina appeared in a radio play which Fellini had written, and she totally identified with his career. He died five months prior to Masina of a heart attack. Masina died of lung cancer on 3/23/1994, Rome, Italy .;</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">McCrindle, Sir Robert</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Scottish Member of Parliament who was returned at the General Election on 6/11/1987.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">McPherson, Aimee Semple</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Canadian-American evangelist who was the first missionary in Hong Kong until her first of three husbands died in 1908. She arrived in Los Angeles in 1918 with $10 and a tambourine and began the International Church of the Foursquare Gospel; within five years she was a top attraction in town. As an evangelist and outstanding showman she offered salvation, healing and baptism, playing to audiences of 5,000 in the $1.5 million Angelus Temple. Throughout her lifetime she set up 400 churches, 200 missions, a Bible college and a radio station. She was often dubbed the "Barnum of Religion."<br /><br />She died of an overdose of barbiturates on 9/27/1944, Oakland, CA.</span></td>
<td class="tg-40k6"><span style="color: white;">B</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Meese III, Edwin</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American Attorney General who was appointed by President Reagan in 1984 and served as a long-time aide. He was first named as a presidential counselor in November 1980, a job which paid $72,200 a year. His appointment became a continual embarrassment to the Reagan administration as he was a highly disorganized public official and seemingly oblivious to ethics. His personal finances were a reckless morass of debts; at one point in 1982 he owed nearly $483,000 in personal loans. He seemed unable to keep his modest personal finances in check, making him a questionable choice for his government position.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Mercator, Gerhardus</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Belgian cartographer, mathematician and surveyor who invented the Mercator map projection and was the most notable geographer of his time. He was famous for building globes that showed the earth and heavens, and won lasting fame with his world map of 1569.After having strokes in 1590 and 1693, he died on 12/05/1594 OS, Duisberg, Germany.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Morinus, Johannes</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">French astrologer who studied philosophy and physics and became absorbed in astrology in Paris. Some of his prestigious clients included Richelieu, de Medici and Louis XIII. He was the author of a magnum opus, "Astologia Gallica," in Latin. Died on 11/06/1656.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Nicholson, Jenny</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American professional astrologer who gained overnight fame when news of her appointment as an advisor to a Union County commission was picked up by API. Commissioners in La Grande, a northeastern Oregon community of about 12,000, came under fierce criticism from the local press and others, after news of the appointment broke on 7/7/1988. Nicholson intended to offer the commissioners astrological guidance without charge, but dropped the appointment instead.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Niehenke, Dr. Peter</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">German astrologer and psychotherapist who has been practicing for 15 years. He conducts self awareness groups and has been a leader in German astrology groups. In 1997 he put out a data collection on disk that repeated data from Gauquelin, Bordoni, Schepel and Rodden, arousing some criticism due to the lack of accurate editing.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Nijinski, Vaslav</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Russian dancer who is noted for being the greatest male dancer of all time, his style being one of high and soaring leaps. He entered ballet school at age nine, and debuted in 1908. In 1913 he married another dancer, Romala. He was hospitalized with hopeless schizophrenia at the age of 28. He died on 4/8/1950, London, England</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Nobuhito Takamatsu, Prince</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Japanese royalty, the younger brother of Emperor Hirohito.</span></td>
<td class="tg-40k6"><span style="color: white;">B</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Pacino, Al</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor, one of the most accomplished stars of his generation who remains a private, enigmatic figure. The only child of Salvatore and Rose Pacino, raised in the mean streets of the Bronx from the time he was two, he is an intense Sicilian. With his mom sick, he dropped out of school at 17 to work as a janitor, movie usher, furniture mover and office worker to bring home an income. His studies at the New York actor's studio led to a small role in "Me, Natalie," in 1969, leading to "The Panic in Needle Park," 1971.<br /><br />When he was selected to play in "The Godfather," 1972, it changed his life forever, not only winning him an Oscar nomination but directing his smoldering, subtle sensitivity into powerful portrayals of complex characters. He won a Tony in 1969 for his Broadway role in "Does the Tiger Wear a Necktie?" and a second Tony for "The Basic Training of Pavlo Hummel." His films include "Serpico," 1973, "Dog Day Afternoon," 1975, and "Scent of a Woman," for which he won an Oscar as Best Actor on 3/29/1993.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Palmer, Arnold</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American champion golfer, a pro from 1954. He won the Masters in 1958, '60, '62 and '64, the British Open in 1961 and 1962, the U.S. Open in 1960, Tournament of Champions in 1962, '65 and '66, Vadon Trophy 1961 and PGA Player of the Year in 1960.<br /><br />During his career, Palmer has won seven major pro tournaments. The son of a golf pro, he had his first club at age three. After serving in the Coast Guard for three years, he won an amateur title in 1959 and turned pro. The first golf millionaire, he lives as spectacularly as he plays. On 7/21/1970 he was named Athlete of the Decade.<br /><br />Married twice; two daughters. He had surgery for prostate cancer 1/15/1997 in Rochester, MN.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Parker Bowles, Camilla</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British news figure as the mistress of Prince Charles, heir to the throne of Great Britain. Known to her friends as Millie, she is the daughter of a wine merchant and a mother who is the daughter of the third Lord Ashcombe. She met Andrew Parker Bowles shortly after her coming-out party at 18, in 1965.She and Prince Charles probably met in the early '70s, some say 1972. They had instant rapport as they both loved horses, fishing, hiking and architecture. They always had a close, comfortable friendship, calling each other Gladys and Fred after a popular TV show. When Charles sailed to the West Indies in 1973, Camilla became engaged to Parker Bowles and they married 7/04/1973. Their son Tom was born in 1974 and daughter Laura, in 1977. Charles was god-father to her son. It was while Charles and Diana were visiting at Camilla's house that they became engaged. Rumors about her affair with Charles came to a head in 1991 when she angrily denied that she had spent the weekend with Charles in Tuscany. After the publication of Andrew Morton's book, she was very upset and tried to keep a low profile. She and Andrew separated in 1992 and divorced before the court in London on 1/21/1995.<br /><br />After Charles and Diana's divorce, the Prince tried to gently include her in his life, having her as hostess at his dinners and gradually being seen together in public. It seemed that any chance that they might ever marry was dashed by the untimely death of Diana on 8/31/1997. However Charles' popularity rating began to increase as he took over the parenting duties of his sons and a more gracious public interaction than formerly. Quite inadvertently, due to a mix-up of schedules, she met Prince William on 6/12/1998. Shaking from nervousness, she sat and drank cool drinks and visited with the poised young Prince, the son of her arch-rival.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Parker, Eleanor</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American actress whose beauty was first spotted by a talent scout at the Pasadena playhouse. She was signed by Warners but her debut scene in "They Died With Their Boots On" ended on the cutting room floor in 1941. Her flaming red-hair showed well in Technicolor and she worked in bit parts and second leads in the '40s. Her best decade of work was in the 1950s from "Caged," 1950 to "Home From the Hill," 1959, before she retired.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Peguy, Charles</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French author, poet and philosopher.<br /><br />He was killed in action in WW I on 9/5/1914.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Pepper, Art</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American musician playing a jazz alto tenor saxophone. He was the star sax player with Stan Kenton's orchestra in the '40s. His career failed when he went too far into drug abuse but he turned it around and rebuilt his reputation before he died on 6/15/1982, Los Angeles, CA.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Ray, Johnny</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American musician who turned to singing when his early ambitions to be an actor failed. He became an overnight success when his second single, "Cry," 1951, went to No.1, making him a bobbysox sensation. As the "Prince of Wails" he stayed on the pop charts with R'N'B until 1959 when he phased into supper clubs and extensive overseas tours. Bi-sexual, he had noted affairs with both men and women.<br /><br />He died of liver failure when he went into a coma 2/22/1990, Los Angeles, CA.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Regulus</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">French astrologer known for his "Dictionnaire Astrologique." Died 10/5/1978, 10:40 AM, Ste. Marguerite, France.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Rehm, Pierre</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French surgeon, a member of Academie Des Sciences.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Rice, Donna</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American news figure, a pharmaceutical company sales representative and part-time actress in Miami in May, 1987 when the news story broke about her Bahamas pleasure cruise with Colorado Senator Gary Hart aboard his yacht, Monkey Business. Except for an interview with Barbara Walters, she never spoke publicly of the affair but dropped out of sight. She resigned her job, her TV commercials were cancelled and she was defamed as a bimbo for fooling around with the married Senator. Offered seven-figure amounts for interviews, she refused; she never made money from the scandal. Though Hart was in the primaries, his hopes for a presidential bid sank like the boat's anchor.<br /><br />Rice faced her loss of position as a spiritual crossroads. She struggled through periods of depression and entered a spiritual twelve-step program about dependency and weakness.<br /><br />Changing her line of work, she began the business of distributing a nutrition product. Spurning commercial offers that came from her notoriety, she did charity work for Human Rights groups.<br /><br />On 5/07/1994 she married Washington DC resident Jack Hughes at Monmouth Plantation, Natchez, TN.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Rice, Greg</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor and realtor who worked with his twin-brother to sell 57 houses their first year in real estate, starting in August, 1977. Three-foot tall, good-looking twins, they have appeared in TV commercials and shows plus a Jerry Lewis movie "Hardly Working." For a short stint, they were co-hosts of a TV game show, "Only the Best," 1982.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Rice, John</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American actor and realtor who worked with his twin-brother to sell 57 houses their first year in real estate, starting in August, 1977. Three-foot tall, good-looking twins, they have appeared in TV commercials and shows plus a Jerry Lewis movie "Hardly Working." For a short stint, they were co-hosts of a TV game show, "Only the Best," 1982.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Rivers, Joan</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American comedienne, thought by many to be the funniest lady on the planet. She certainly has one of the fastest, most agile minds in show biz. Her rapid fire mix of gossip, insults, flaunting of taboos and ridicule of flaws and neurosis is written 90% by her. She also wrote comedy for Candid Camera, scripts and material for Phyllis Diller and Zsa Zsa Gabor and humor books. Her autobiography "Enter Talking" was written with Richard Meryman, Delacorte Press, 1986.<br /><br />The younger of two daughter of Russian-Jewish refugees, she learned from her doctor dad to crack a joke and was making people laugh by the time she was 11. She learned from her mom that rich was better than poor, and raised with privilege and a good education. Rivers married Jimmy Sanger in 1957 and had it annulled the following year when she decided she wanted to be an actress, not a housewife. While doing off-Broadway, she worked in offices and turned to comedy in 1960 to supplement her income.<br /><br />By 1965 she was told that she was too old and passed over. A week later she was booked on Johnny Carson's "Tonight Show." They clicked. Their immediate rapport was a hit with the audience and she appeared for years with Carson before hosting her own "Late Show Starring Joan Rivers," with a contract for $10 million over three years. She moved into the stratosphere as America's top comedienne, the darling of the circuit with tours, magazine covers, nightclub and Las Vegas gigs, TV projects, books and records.<br /><br />With the cosmetic surgery she had over the years she looks fabulous, blonde, sleek and chic.<br /><br />Rivers married Edgar Rosenberg, who later was the executive producer of her show, on 7/15/1965. Their daughter Melissa was born in 1969. On 8/14/1987, Rosenberg committed suicide.</span> </td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Russell, Ken</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">British film director who aimed to shock, which he did with flair but no subtlety. Beginning as a dancer, actor and photographer, he apprenticed in a rigorous training in BBC art films, after which he turned out to be a middle-aged <b>infant terrible</b> of the '70s. His work included "French Dressing," 1964, "Women in Love" 1969 and "The Devils," 1971. Russell made two marriages; six kids.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Sanders, George</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Russian-born American actor who won a Best Supporting Actor Oscar for his role in "All About Eve," 1950. He was known for his rude, cynical and often disagreeable demeanor; Sanders was easily type-casted as the witty heavy or dedicated crank. He appeared in 90 films from 1936. Among his works were the favorites, including "The Ghost and Mrs. Muir," "The Picture of Dorian Gray" and "A Shot in the Dark." He was born to British parents living in St. Petersburg. When he was age 11, he and his parents fled back to Britain during the communist revolution. On 4/25/1972, in a hotel room in Castelldefels, Spain, Sanders committed suicide by swallowing five bottles of Nembutal. He left behind a note saying "Dear World, I am leaving you because I'm bored. I feel I have lived long enough. I am leaving you with your worries in this sweet cesspool and good luck."</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Sayako, Princess</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Japanese royalty, the daughter of the Emperor Akihito Heisei and Michiko Shoda, the granddaughter of Emperor Hirohito. A modern woman, she studied to become an ornithologist.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Scicolone, Maria</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Italian noted family, the younger sister of actress Sophia Loren. She was married to Romano Mussolini on 3/03/1962; two daughters. They separated in 1970 and divorced in 1975. She was married a second time in 1977 to an Iranian doctor from whom she later separated.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Sexton, Mason S.</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American astrologer, Wall Street forecaster.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Spielberg, Steven Allan</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American film producer and director, the winner of an Academy Award on 3/21/1994 for his direction of the Best Picture of the year, "Schindler's List." Spielberg started tinkering with film production when he was eight with his dad's 8mm camera and became a professional director by the time he was 20 for Columbia Pictures. The most successful man of the '80s and the most successful director in history, he achieved notoriety and wealth with such film greats as "Jaws," "Close Encounters of the Third Kind," "E.T." "Raiders of the Lost Ark" and the blockbuster, "Jurassic Park." Spielberg also produced several films as well as dabbling in TV production; with interests from cartoons to serious adult themes. He was acknowledged as a giant amongst the Hollywood elite and was given notable respect for his many achievements. Spielberg married Amy Irving 1986-1989 with one son, Max; the marriage was terminated with a settlement of over $100 million. He then started a relationship with Kate Capshaw; they married on 10/12/1991. As of 1998, they had six children including Max and several adopted kids.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Staubach, Roger</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American football quarterback, one of the all-time greats, winner of the Heisman Trophy 11/26/1963. A devout Roman Catholic, he had a squeaky-clean image. Color blind; fiercely competitive; he broods over losses. He played with the Dallas Cowboys in 1969, and retired in April 1980.<br /><br />Doing a stint in the U.S. N.R. 1965-69, he did a Vietnam tour. On 9/04/1965 he married; five kids.<br /><br />In 1985 Staubach was elected to the Football Hall of Fame.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span> <br /></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Stern, Melissa</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American news figure, the child of a surrogate mother who kept her. Her mother, Mary Beth Whitehead, was the surrogate mother by contract for a 40 year-old and childless father, William Stern, and his wife. Melissa was named Sara by her surrogate mother, but removed by court order to the temporary custody of her father who filed suit for breach of contract. Lasting for two years and bitterly fought, the custody case went all the way to the New Jersey State Supreme Court. When all was said and done, Stern was awarded custody on 3/31/1987. The case was a precedent-setting trial for the legal and moral questions of surrogate parenting. Stern's victory was not total, though, as Whitehead was granted visitation rights twice a month to her "daughter." Melissa has been raised with full knowledge of the story and calls both her surrogate and biological mothers, "mom."</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Stokowski, Leopold</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">British-American famed conductor, violinist and organist by the age of 16. He emigrated to the U.S. in 1905 and began to conduct in 1908. Stokowski worked at the Cincinnati Symphony from 1909-1912, the Philadelphia Orchestra from 1914-1926 and the New York Symphony from 1944-1945. He was married to Gloria Vanderbilt. Died on 9/13/1977, Hampshire.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Stone, Steve</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American baseball pitcher, 5'10", 175 lbs. who made his debut with the San Francisco Giants 4/08/1971. He later became a sportscaster.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Strehl, Jack</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American entrepreneur, an electrical engineer who built a national semi-conductor company in Silicon Valley. He sold the big business around 1980 and retired to full-time playing, interests in airplanes, hi-speed auto racing and many other interests. Once married, he is now divorced.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Sullivan, Erin</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Canadian astrologer, the president of the Victoria Island Astrological Society. She is known as an innovative leader in a modern psychological approach to astrology and a member of the AFAN Steering Committee. Her book, "Saturn In Transit," has been published in Portuguese, Spanish, German and English; she has also authored four other books. In both Canada and the U.S., awards and commendations have been bestowed upon her for her work on Media Watch for AFAN. An international speaker, Sullivan is world traveled, speaking at renowned seminars and conferences. In the winter and spring months she lives in Scottsdale, AZ and in the summer and autumn months in London, England. In 1989 she lived solely in Oxford, England. She has two grown daughters and one grandchild.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Swinburne, Algernon</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British poet of the Pre-Raphaelite movement who, unconventional in his views and personal life, shocked society with his work, "Poems and Ballads." He also caused society to drop its jaw with his play, "Atalanta In Calydon." Known as a masochist who loved to be flogged, he was suspected of being a homosexual, although no hard evidence was present. Dissipation undermined his health and he lived a quiet life after 1880.<br /><br />Died on 4/10/1909, London, England.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Tailleferre, Germaine</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French woman composer who was the only woman member of the group of young composers, "The Six." She composed her first piano piece at the age of five and started her piano concerto performances in Europe and the U.S. in 1924. From 1942-1946, she lived in the U.S., teaching and composing. Blessed with natural grace, her music was composed with charm, spontaneity and freshness.<br /><br />She married twice; her first husband, Ralph Barton 1925-31, committed suicide shortly after their divorce. Her second husband was a French lawyer; one daughter.<br /><br />It was not an easy life, she had to work hard to keep up her creative output and survive financially.<br /><br />In her 90s, Tailleferre was still spry and youthful, living with a granddaughter, two cats and a dog.<br /><br />She died 11/07/1983, Paris, France.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Techter, David</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American parapsychologist and museum worker in charge of fossil vertebrae at Chicago Natural History Museum from 1955. He received his geology degree from Yale and is a member of Society of Psychical Research. Conducting research tests for ESP in school children, he has written reviews and published a biographical index of these studies.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Urban, Hubert Josef</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Austrian parapsychologist, author and professor of neuropsychiatry who, as an M.D., conducted special studies in neurology, neurosurgery, neuro-anatomy and psychiatry in San Francisco, Paris, Stockholm, Breslau and Buenos Aires. From 1938 on, he served as a professor of neuropsychiatry at the University of Innsbruck in Austria. In addition, he visited India for field work in psychiatry and to investigate cases of psi phenomena, as well as to do experimental work in parapsychology. Throughout his career he held a particular interest in telepathy, clairvoyance, mediumship and the investigation of ESP before, and after, electro-shock treatments. As the author of 52 publications in the fields of neurology, psychiatry and parapsychology, he wrote the book "Parapsychology and Psychiatry," 1946, as well.<br /><br />He was married in 1934 and had five daughters and two sons.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Van Runkle, Theodora</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American costume designer for movies, an Oscar-winner. Educated at Choinard Institute in Los Angeles, she moved into film work, making her debut in 1967. She was especially noted on period films such as "Bonnie and Clyde," as well as Coppola's "The Godfather Part II," and "Mame," 1974, and "New York, New York," 1977.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Vlady, Marina</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">French actress, an exquisite blond of international fame. A graceful and intriguing leading lady, she won the best actress Cannes Award for the Italian film, "The Conjugal Bed." She originally made her film debut at the age of ten after completing ballet training.<br /><br />Acting runs in the family, as her two sisters are also actresses. She was married and divorced from Robert Hossein, her director and co-star from "The Conjugal Bed."</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Volman, Mark</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American musician, singer and songwriter, one of the two leaders of the "Turtles," a big group in the '60s that had about eight big hits. After the group disbanded, they went on as Flo & Eddie, working with Frank Zappa's "Mothers of Invention." They also did a Ringo Starr flic entitled "200 Hotels."</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Walters, Barbara</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American broadcaster who began her career in 1954 when she joined the staff of the "Today" show. After 20 years experience, she signed a five year contract with ABC in 1975 as a newscast anchor woman at a salary of one-million dollars a year. She is a successful, cool and intelligent woman with a caring demeanor.<br /><br />As the daughter of a vaudeville booking agent with a flamboyant personality, she was raised in the environment of entertainers and witnessed the opening of Boston's first Latin Quarter nightclub, which made her dad wealthy within two years. She learned at the same time that fame and money come and go. She was given the advantage of a Sarah Lawrence education, and toured the continent.<br /><br />She had an older brother who died when she was three years old and an older sister who was born handicapped. Through their ups and downs, her family remained extremely close.<br /><br />Walters has been married twice, first to theatrical producer Lee Gruber for nine years. The couple were childless until they adopted a daughter in 1968. Her second marriage was to Merv Adelson in 1986; they separated in 1990 and divorced on 8/17/1992 in Los Angeles, CA.<br /><br />Most recently she has been an anchor on ABC's news magazine "20/20," and has her own daytime discussion show entitled "The View."</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Warhol, Andy</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">American underground artist and film maker who had a genius for creating attention. An androgyne and voyeur himself, his salon became the New York center of the freak scene in the '60s. When the pop-art movement exploded at the end of 1962, his drawings of soup cans and screens of the famous became hot property. On 6/03/1968, he was shot by some nut-lady; after his recovery he was somewhat subdued, but still newsworthy in the '80s for his personal outrage of convention and abberative entourage. On 2/21/1987 he had a gall bladder operation and died the next morning of a heart attack, on 2/22/1987. His estate was estimated to be worth $220 million.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Watson, Charles "Tex"</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American homicide who, on 8/09/1969, while under the orders of Charles Manson, stabbed eight-month pregnant Sharon Tate to death as Susan Atkins held her. He also was involved in the La Bianca killings. After his trial, Watson was sentenced to life in prison, where he claimed to have found Jesus; he preaches one sermon a month in prison.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Whittaker, Roger</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">British singer born in British South Africa who is a very popular recording artist in Britain, Canada and the U.S.</span></td>
</tr>
<tr>
<td class="tg-s7xz"><span style="color: white;">Wilson, Richard</span></td>
<td class="tg-s7xz"><span style="color: white;">Air</span></td>
<td class="tg-s7xz" colspan="2"><span style="color: white;">Scottish actor, well known for his role as Victor Meldrew of "One Foot in the Grave."</span></td>
</tr>
<tr>
<td class="tg-mlny"><span style="color: white;">Wilson, Wendy</span></td>
<td class="tg-mlny"><span style="color: white;">Fire</span></td>
<td class="tg-mlny" colspan="2"><span style="color: white;">American noted family, one of Brian and Marilyn Wilson's two daughters. In 1989 she played in the band "Wilson Phillips" with sister Carrie and singer Chynna Phillips. The band received three Grammy nominations in 1991 and released an album entitled "Shadows and Light," in 1992, which sold 1.4 million copies; their debut LP sold eight million copies. However, the band was defunct by 1994.<br /><br />Her parents were divorced in 1979 and she had a cool relationship with her father. He was very caring when she and her sister Carrie were little kids but only called twice a year by 1991. Still in the process of finding herself, Wendy frequently changes her style and hair color. She and her sister are close, with the same tastes.</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Carla, Wilza</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">Brazilian actress who worked in burlesque as a beautiful young woman. However, she gained immense weight that changed both her figure and face and she moved into comic roles on TV.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Woodman, Marion</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Canadian psychologist, renowned speaker and writer</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-8wvm"><span style="color: white;">Wright, Marion</span></td>
<td class="tg-8wvm"><span style="color: white;">Earth</span></td>
<td class="tg-8wvm" colspan="2"><span style="color: white;">American cellist who took lessons from the age of 11 and played with the Indiana Philharmonic. In addition, she played with the Nashville Symphony for two years and the Kentucky Wesleyan College quartet for three years. A Mensan, she married in 1943; three kids.</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Wulfing, Sulamith</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">German painter who specialized in nature and romance-fantasy subjects, such as centaurs and magical lands. Many of her works have been reproduced on letters and post cards. "The Mystical Art," has been published containing her complete work, as well as extensive biography and many photos.</span></td>
<td class="tg-40k6"><span style="color: white;">A</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Zampa, Luigi</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">Italian film director whose work includes "Vivere in Pace" in 1946.<br /><br />Died after a long illness 8/15/1991, Rome.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Zemach, Margo</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">American artist, a children's book illustrator. Zemach won the Calldecott medal in 1968, and completes one or two books a year.<br /><br />She married on 1/29/1957, and has four daughters.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
<tr>
<td class="tg-40k6"><span style="color: white;">Ziegler, Karl Waldemar</span></td>
<td class="tg-40k6"><span style="color: white;">Water</span></td>
<td class="tg-40k6"><span style="color: white;">German chemist and co-winner of the Nobel Prize in Chemistry in 1963 for discovery of polyethylene plastics.<br /><br />Ziegler died 8/12/1973 Mulheim, W. Germany.</span></td>
<td class="tg-40k6"><span style="color: white;">AA</span></td>
</tr>
</tbody>
</table></div></div>
If we tabulate this, we note that the number of people entirely lacking each element is:
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<thead>
<tr>
<th class="tg-wa1i">Element</th>
<th class="tg-wa1i">Number entirely lacking</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-p6pl">Fire</td>
<td class="tg-0ppk">2</td>
</tr>
<tr>
<td class="tg-e4fp">Earth</td>
<td class="tg-pnfo">49</td>
</tr>
<tr>
<td class="tg-6gy8">Air</td>
<td class="tg-940v">25</td>
</tr>
<tr>
<td class="tg-awjh">Water</td>
<td class="tg-mfjg">80</td>
</tr>
</tbody>
</table>
As we can see, only two public figures are shown with a complete lack of fire, yet eighty show complete lack of water! This result obviously is biased, and several features of AstroSignature explain this:<div><ol style="text-align: left;"><li>It is practically impossible to have no planets and the Ascendant in fire without having planets in fire houses. When the fire element is empty and not on the Ascendant, unless a second element be empty, at least some planets will most likely be in fire houses. This is because whenever planets and the Ascendant are in the same element, those planets are almost certain to lie in fire houses</li><li>Under the AstroDataBank scoring system <i>deductions</i> occur for Earth due to flowing Neptune aspects and for Water due to flowing Saturn aspects, but for Fire and Air no aspects from any planet cause deductions in the elemental score.</li><li>Under AstroDataBank, the low element list had (essentially) the same score for all elements, whereas the <i>high</i> element list had different scores adjusted to what was observed for each different element.</li></ol><div>There exist other problems with AstroDataBank’s studies from a purely astrological perspective:</div></div><div><ol style="text-align: left;"><li>House positions of planets can vary depending upon which system is used, yet no statement is made about this in the discussion</li><li>The South Node is listed only in houses, although it remains in each sign for only about eighteen months and its sign position could never be called “generational” — so why was its sign position not listed as scoring (with perhaps an equivalent point deduction for the North Node)</li><li>Again with the South Node, whether mean or true was used is not noted</li></ol><div>The differences between house systems can be seen by comparing the Placidus, Campanus and Equal charts for Algernon Swinburne — noted by AstroDataBank for lack of earth and also for excess fire:</div></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDZIv7BsplrNbY5ANjUu3jfZaANfZlTIiU0uZgCFwAu5CEC17kkedtzLJNpYorbGREpoOQHjMQBNNYJOg0ZudSOWl_KH2-kVV_yE2ZwCX_A7QZ3NrlTSY40ZKpQPi1bvjgxeLNIymXDBkZNMRojo7I2OBfJXUmpuziCSS_XGB4UrpAdia1DuQia6Y5/s1102/Algernon%20Swinburne%20Placidus.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1102" data-original-width="748" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDZIv7BsplrNbY5ANjUu3jfZaANfZlTIiU0uZgCFwAu5CEC17kkedtzLJNpYorbGREpoOQHjMQBNNYJOg0ZudSOWl_KH2-kVV_yE2ZwCX_A7QZ3NrlTSY40ZKpQPi1bvjgxeLNIymXDBkZNMRojo7I2OBfJXUmpuziCSS_XGB4UrpAdia1DuQia6Y5/s16000/Algernon%20Swinburne%20Placidus.png" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Placidus chart for Algernon Swinburne. Note extremely strong fire emphasis and lack of any planet in an earth sign or house</td></tr></tbody></table><br /><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcN7lP9mn1PoHUNfvb9VKsLG2tTEsiGKsMJwQLraFU0RNLJwfT9xugSu8Y1Jg-RtBcFqsiOnRzrlHyYaCJECSR-S6qBpytaFDSL7Lj-DAeFS4IQIgM8EZVkAsW9CJ7BBSmM5f9YR0eCFJEjhqSpOm9X0brsK3gL4Rkx82a-h0EiZWRnq6syIlsR0_S/s1102/Algernon%20Swinburne%20Campanus.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1102" data-original-width="748" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcN7lP9mn1PoHUNfvb9VKsLG2tTEsiGKsMJwQLraFU0RNLJwfT9xugSu8Y1Jg-RtBcFqsiOnRzrlHyYaCJECSR-S6qBpytaFDSL7Lj-DAeFS4IQIgM8EZVkAsW9CJ7BBSmM5f9YR0eCFJEjhqSpOm9X0brsK3gL4Rkx82a-h0EiZWRnq6syIlsR0_S/s16000/Algernon%20Swinburne%20Campanus.png" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Campanus House System chart for Algernon Swinburne. Note that here the fire emphasis is a little weaker because Mars and Jupiter are in the Sixth (earth) House</td></tr></tbody></table><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi63-cGubLVHH-MgThHntqukxqIQOsdSq8LKyUJXm5KwBag2dFK12XwMC54UTZucQgQZJItJXtX0Lh4WG5Uaun4ZPBvC2Xz4-z1t1ZvvBmTOcJ3zE6u0lNRufbGNaiSoHQVq4T_eNEfWepzu2g5boh2srr8_KskriI8WWouvUW1hWi-uk5lh4HkQRIW/s1102/Algernon%20Swinburne%20equal.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1102" data-original-width="748" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi63-cGubLVHH-MgThHntqukxqIQOsdSq8LKyUJXm5KwBag2dFK12XwMC54UTZucQgQZJItJXtX0Lh4WG5Uaun4ZPBvC2Xz4-z1t1ZvvBmTOcJ3zE6u0lNRufbGNaiSoHQVq4T_eNEfWepzu2g5boh2srr8_KskriI8WWouvUW1hWi-uk5lh4HkQRIW/s16000/Algernon%20Swinburne%20equal.png" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Equal House chart for Algernon Swinburne. Note the major differences from Placidus and Campanus, and that the fire emphasis is comparable to that in Placidus — which of course will not be true for other charts with similar Midheaven positions</td></tr></tbody></table>Whilst the precision and relative simplicity of the AstroDataBank scoring system can be commended, and the lists were and are — like so many lists for me — fascinating, the problems discussed above are difficult to easily address even if I will confess to not thinking about it seriously.jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-27267454266679925312022-11-19T14:10:00.232+11:002023-06-21T12:23:44.029+10:00“Successive ducks” not always what it is said to be<p>In his 2001 <b><u>Wisden</u></b> obituary, Holcombe “Hopper” Read, an amateur fast bowler who had a short but successful cricket career in the middle 1930s, was said to have made “eight successive ducks”. Whilst Read was an exceptionally poor batsman — indeed his career average of 3.67 remains the lowest by any Test cricketer ever, and he scored in a mere 22 of his 58 first-class innings in England — it is actually not true that Read ever suffered eight successive <i>ducks</i>, that is, <i>eight consecutive innings in which he was dismissed without scoring</i>.</p><p>In fact, no batsman in first-class cricket has ever suffered eight consecutive innings dismissed without scoring, or even seven consecutive innings dismissed without scoring. What Read actually suffered was <i>eight consecutive innings without scoring</i>, but <i>one of these was not out</i>. Six consecutive innings dismissed without scoring <a href="https://stats.acscricket.com/Records/First_Class/Overall/Batting/Most_Ducks_in_Consecutive_Innings.html">has occurred twelve times</a>, although most of these have occurred since 2000 in the subcontinent. There was only one between 1908 and 1986, by Victor Cannings in his last innings of 1957 and first five of 1958.</p><p>In contrast to the relatively small records for consecutive ducks, records for <a href="https://stats.acscricket.com/Records/First_Class/Overall/Batting/Most_Consecutive_Innings_without_Scoring.html">consecutive scoreless innings</a> extend to as many as twelve by Mark Robinson — ironically during the “Year of the Bat” in 1990 (due of course not to the quality of the batting but to abysmal English bowling and rigged pitches). For a long time the record was nine, but Jim Griffiths in the middle 1970s broke the record with ten consecutive scoreless innings over four seasons, and then came Robinson.</p><p>What is especially notable is that the two sequences are mostly unrelated to each other, especially the sequences of scoreless innings. Only the following seventeen sequences are in both, of a total of over 150 sequences of at least six scoreless innings:</p>
<table style="width: 595px;">
<tbody>
<tr>
<td width="57">
<p>#</p>
</td>
<td width="117">
<p>Type</p>
</td>
<td width="224">
<p>Player</p>
</td>
<td width="198">
<p>Season(s)</p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>8</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>C.E. Shreck</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2015</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2015</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>7</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong><a href="https://www.espncricinfo.com/player/ian-kidson-45894">I.M. Kidson</a></strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1987/1988 - 1988/1989</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1987/1988 - 1988/1989</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>7</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>R.R. Richards</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2011/2012 - 2012/2013</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2011/2012 - 2012/2013</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>9</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong><a href="https://www.espncricinfo.com/player/paul-garlick-13534">P.L. Garlick</a></strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1984</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1984</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>9</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>D. Ramnarine</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2001/2002</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2001/2002</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>8</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>T.S. Parankusam</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1938/1939 - 1942/1943</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1939/1940</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>8</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>Abdul Ghaffar</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2010/2011 - 2011/2012</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2010/2011</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>7</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>Raza-ul-Hasan</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2021/2022</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2021/2022</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>W. Mead</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1901</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1901</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>J.A. Hayes</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1954/1955 - 1955/1956</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1954/1955</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>R.W. Hanley</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1983/1984</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1983/1984</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>Aaqib Javed</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">1988/1989 - 1989/1990</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">1989/1990</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>S. Javed</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2000/2001 - 2001/2002</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2001/2002</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>R.R. Bose</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2002/2003 - 2003/2004</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2002/2003 - 2003/2004</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>Umar Farooq</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2015/2016 - 2016/2017</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2015/2016 - 2016/2017</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>6</strong></p>
</td>
<td style="background-color: #757171; width: 117px;">
<p><strong><span style="color: white;">Scoreless</span></strong></p>
</td>
<td rowspan="2" width="224">
<p><strong>Mohammad Mudhasir</strong></p>
</td>
<td style="background-color: #757171; width: 198px;">
<p><strong><span style="color: white;">2017/2018</span></strong></p>
</td>
</tr>
<tr>
<td width="57">
<p><strong>5</strong></p>
</td>
<td style="background-color: #c00000; width: 117px;">
<p><strong><span style="color: white;">Ducks</span></strong></p>
</td>
<td style="background-color: #c00000; width: 198px;">
<p><strong><span style="color: white;">2017/2018</span></strong></p>
</td>
</tr>
</tbody>
</table>What this reflects, of course, is that the very worst batsmen, like Griffiths or Francis McHugh, are unlikely to be out on every visit to the wicket because they frequently to not get the opportunity to be so much as dismissed. Such batsmen are so much a liability that any partner will naturally attempt to prevent them ever giving them the strike if at all possible, which can easily mean they get out themselves. It is true that Ian Kidson, linked above, has probably the most innings (37) of any first-class cricketer with a worse batting average than McHugh, and that but for his stint with Northamptonshire against already very weak English bowling Hanley would have had a higher ratio of wickets to runs in his career than Bhagwat Chandrasekhar or Alf Hall. On the other hand, Walter Mead hit a century against Leicestershire in 1902.<div><br /></div><div>So, the message is to be careful about claims of “successive ducks” — on one occasion, <b><u>Wisden</u></b> made a critical mistake!</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-46203560951562007682022-10-28T21:03:00.148+11:002022-11-23T22:10:03.090+11:00Is Wisden consistent in what it calls “fair”?<p>Over recent weeks, my brother has argued that uncovered pitches, even in the Enriched nations of England and New Zealand, are inherently less fair than covered pitches because they are capable of producing conditions excessively favourable to spin bowlers. My brother and mother have said that these conditions bred spin bowlers who could not adapt to the cast-iron wickets that prevailed on the ancient soils of Australia.</p><p>The late David Green in his early 2000s ‘Back to Grass Roots’, contrariwise, argued that covered pitches given spin bowlers so little opportunity that they stereotype the game — eliminating opportunities for many men who otherwise would have a chance of a successful career. Green’s argument to me is very reasonable for reasons I may have discussed elsewhere on this blog, but which would be off-topic to discuss here.</p><p>One significant observation is that before widespread covering — not to mention limited overs cricket — made conditions excessively tough for spin bowlers, England did possess one ground where spin bowlers struggled just as much as they do on today’s covered pitches. In the immediate post-World War Two years, when the proportion of overs bowled by spinners peaked, <i>Trent Bridge</i> was an outstanding exception. Whilst almost every other county team relied upon attacking spinners who — although even in England hopeless against the Australian batsmen with the footwork and power to smash ball after ball — drew huge crowds, Nottinghamshire relied largely upon the medium-fast seam of the injury-prone but classy Harold Butler and the more robust though less skilled Arthur Jepson. Spin bowlers who were successful at almost all other venues in England were typically hopeless at Trent Bridge.</p><p>In this era, <b><u>Wisden</u></b> was quite clear that the pitches at Trent Bridge were <i>far less fair</i> than pitches at other grounds in England. The almanac judged them as excessively unfair to bowlers in general, not merely to spinners. However, by the logic of my mother and brother, the Trent Bridge pitches would have to be considered <i>fairer</i> than those at other venues, especially as they were difficult for pacemen as well as spinners, whereas David Green, Mike Selvey and others lamenting the decline of spin bowling often noted how easy 1980s and 1990s English pitches were for pace and seam. My mother and brother were clear that the Australian pitches upon which almost every old English spin bowler failed completely were actually fairer than English pitches of the era, because they were much less likely to give spin bowlers extreme assistance.</p><p>To assess this question, we must note that in the very era when English spinners were most consistently failing in Australia, Australia itself produced numerous outstanding spin bowlers. Harold Hordern, Bert Ironmonger, Arthur Mailey, Clarrie Grimmett, Bill O‘Reilly and Leslie Fleetwood-Smith constitute a set of spin bowlers seldom equalled by any country over a comparable span. Contrariwise, Nottinghamshire as of 1950 — when <b><u>Wisden</u></b> was at its most vocal about the Trent Bridge pitches — had not provided a significant spin bowler since Sam Staples three decades previously. Indeed, even relative to the drastically diminished wicket hauls attained by spin bowlers since covering was increased in 1959, there has not been a significant spin bowler hailing from Nottinghamshire ever since. Every one of Nottinghamshire’s most successful spin bowlers since Staples retired in 1933 — Bruce Dooland, Gamini Goonesena, Bryan Wells, Eddie Hemmings — was an import recruited with a substantial reputation. So were lesser lights like Ken Smales, Michael Morgan, Robert White and Harry Latchman. By the end of the 1990s, England, as Green noted, had the same complete incapacity to produce and develop spin bowlers Nottinghamshire did at mid-century. This, as Green noted, really <i>does</i> point to modern pitches being quite unfairly rigged against the spinner.</p><p>From another angle, old <b><u>Wisden</u></b>s never said interwar Australian pitches were unfair even though the English spin bowlers who could adapt to them can be counted on one hand. More deeply, <b><u>Wisden</u></b> could be said to <i>maintain a clear contrast between nature and nurture</i>. The radically different Australian soils — four-and-half orders of magnitude older than English soils — mean that it is <i>natural</i> that English bowlers would struggle to cope because grass and soil fauna interact in completely different ways and consequently the way in which they bind is naturally radically different. Contrariwise, the mid-century Trent Bridge pitches, and modern covered pitches throughout England, reflect artificially prepared surfaces that have the effect of producing conditions that must be called rigged against spin bowlers.</p><p>Thus, what David Green was effectively saying in the early 2000s is very consistent with what <b><u>Wisden</u></b> had said about Trent Bridge pitches half a century previously. It is also more consistent than many other issues the almanac has had to cover over a long period.</p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-19423489827032737912022-10-23T19:34:00.203+11:002023-05-08T19:50:31.767+10:00What should have been the first covering ban<p>Throughout <b><u>Wisden</u></b>s between 1985 and 2001, the editorials outcry covered pitches as destroying the virtuosity found in earlier English batting, and greatly reducing the amount of spin bowling. As a teenager in the early 1990s, I was attracted powerfully by the match and season wicket hauls seen in older English cricket, which reached up to three times what the top English bowlers were taking when I discovered them. <b><u>Wisden</u></b>, and consequently myself, assumed that the primary reason was that the older bowlers were vastly more skilled, with skills outside of containment being lost with the advent of one-day cricket, although I was already aware that pitches had become more unfavourable to spin bowlers with the advent of covering.</p><p>With the 1998 <b><u>Wisden</u></b>’s ‘Woodcock’s Hundred’ and David Green’s 2002 ‘Back to Grass Roots’, it became clear to me that the old English spin bowlers who took huge wicket hauls were not as good as previously presumed — or at all events, unlikely to have been more successful than what spinners remained then. Although Green was too tactful to say so, he demonstrated that modern covered pitches were unquestionably <i>rigged against spin bowlers</i>, whilst Woodcock’s list of the 100 greatest cricketers of all time included only three of the thirteen bowlers with over 2,500 first-class wickets, and all of these largely for their <i>batting</i>. It occurred to me that almost every old English spin bowler was hopeless on Australian pitches — the number who were even relatively as successful in Australia can be counted on one hand.</p><p>However, Green’s point — which I accepted — that batting techniques had further deteriorated from those Woodcock lamented in 1985 made me believe uncovered pitches must produce far superior technique. As early as the 1956 Ashes tour, Bruce Harris on page 20 of his <b><u>Defending the Ashes: 1956</u></b> said that</p><blockquote><p style="text-align: center;">“Maybe it will help if, for a change, the Australians allowed the “gentle dew from heaven” to drop upon the place beneath, even when that place is a cricket pitch”</p></blockquote><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOGKZ3_oUK-Jeb-RpO9A4H5zP-L77b_cxC_J1i58rOy49HzuapCynVEy0X0toVcMyAwpv2I5bgsL-jokVl5f15nTuPlgJSYDA4lrsQ5RZkPAKOBILuFXGdYmLMKTFNJJIIs6MbUly6JrUiK5TsZ4Ro-oz6WFVK2kxZQ5HvU0jMAVPuFj6oGUsp5ShA/s1027/381675044.png" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1027" data-original-width="684" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOGKZ3_oUK-Jeb-RpO9A4H5zP-L77b_cxC_J1i58rOy49HzuapCynVEy0X0toVcMyAwpv2I5bgsL-jokVl5f15nTuPlgJSYDA4lrsQ5RZkPAKOBILuFXGdYmLMKTFNJJIIs6MbUly6JrUiK5TsZ4Ro-oz6WFVK2kxZQ5HvU0jMAVPuFj6oGUsp5ShA/w266-h400/381675044.png" width="266" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Harris’ call for uncovering on page 20 of this book was two years too early. If he had seen the 1958 New Zealand tour he would (ought to!) have made a far more rigorous call for complete abolition of covering </td></tr></tbody></table><br />Undoubtedly, Harris wrote two years prematurely. In 1958, New Zealand averaged an abysmal 12.49 runs per wicket in five Tests, with Tony Lock averaging 7.47 runs per wicket. At the same time, the Kiwis were so atrociously weak in spin bowling that in the Third and Fifth Tests, they failed totally to exploit favourable conditions. Since soils in New Zealand are much closer to soils in England than to soils in Australia, and New Zealand pitches are in no way physically dangerous after rain, ever since reading <b><u>Defending the Ashes: 1956</u></b> I have felt that Harris, or anyone who wrote a book on that 1958 tour, should have taken a rigid stand against <i>any and all pitch covering</i> in New Zealand.<div><br /></div><div>From a modern perspective, New Zealand stood a few years ahead of the English curve. Domestic New Zealand cricket at that time was dominated by short-of-a-length medium pace bowlers under largely covered pitches and lush, heavily fertilised outfields that were increasingly unfavourable to spinners. This meant that New Zealand’s batsmen gained absolutely none of the skill required to handle quality spin under less unfavourable conditions. The situation of New Zealand in 1958 reminds me a great deal of English cricket thirty years later: conditions made for easily mastered medium-pace seam bowling but which precluded developing skill against speed or especially spin of reasonable class. Completely and uncompromisingly eliminating covering (except perhaps pitch ends) both before and during matches would undoubtedly have made it easier for New Zealand to develop spin bowlers, who should have improved the public appeal of cricket and possibly the team’s abysmal batting.</div><div><br /></div><div>From another angle, if England had seriously asked about the 1958 New Zealand team questions like:</div><div><ol style="text-align: left;"><li>why did they fare so much worse than on their previous 1949 tour?</li><li>why had their batting been so inept against spin over the previous half-decade?</li><li>why did they have zero spin bowling of their own to exploit favorable pitches?</li><li>what in New Zealand domestic cricket and society was making decent batsmen and spinners impossible to develop?<br /></li></ol></div><p>the English could potentially have learned more than from any other touring team in history. England in 1958 was beginning to do exactly what New Zealand had been doing for some few years previously:</p><ol style="text-align: left;"><li>creating lush outfields and overgrassed pitches</li><li>increasing covering of pitches<br /></li><li>seeing a dramatic reduction in attendance-attracting spin bowling</li><li>reducing the skill of their batsmen</li></ol> The results, whether from the 1958 New Zealanders or the 1989 England team, are highly instructive: teams that, to paraphrase Kyle Wright, “were bad and were boring”.jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-45271557971719419462022-10-23T14:42:00.082+11:002022-11-02T00:25:59.585+11:00The “immigration gap” in settler nations<p>Today, discussing the fate of the VFL’s “soccer belt” problem children in 1960s — <span style="color: red;">South Melbourne</span>, <span style="color: #2b00fe;">North Melbourne</span>, <span style="color: #2b00fe;">Footscray</span> and <span style="color: #660000;">Fitzroy</span> —one thing occurred to me whilst I was discussing with my brother and a former Penleigh friend the southern and eastern European immigration that eroded those clubs’ supporter bases. I had long presumed this post-World War II migration wave to be largely driven by migrants fleeing Stalinism, although a large proportion was from non-Stalinist Greece and Italy.<br /></p><p>An oddity is that, whilst there was large-scale migration from:</p><ol style="text-align: left;"><li>the northern Stalinist nations of the Baltic States, Poland, the former Czechoslovakia, and Hungary and<br /></li><li>the Balkan nations of the former Yugoslavia, Greece and Albania</li></ol><p>there was, at least before Stalinism collapsed, very little or no migration from the intermediate nations of <i>Romania</i> and <i>Bulgaria</i>. My brother agreed with me on this — he knew people from Greece, Yugoslavia and the countries listed in (1), but no one of Bulgarian ancestry and only one person of Romanian ancestry. Looking at Wikipedia, although the figures are substantially distorted by migration since the collapse of Stalinism, one does see how small the Romanian and Bulgarian diasporas in Australia remain.</p><p>A similar situation prevails on the opposite shore of the Black Sea. There is virtually no (Stalinist-era or earlier) <i>Georgian</i> diaspora in Australia or other colonial settler nations, but large <i>Armenian</i> diasporas.</p><p>This interesting fact my brother suggested to be because it was easier to emigrate from Yugoslavia and Greece than from Stalinist nations more closely connected to Russia. However, as we discussed, that makes little sense because Enver Hoxha’s Albania was much harder to migrate from than Russia-allied Stalinist countries, yet still saw significant migration.</p><p>What my brother did point out was that the lack of pre-existing communities may have prevented immigration from Romania, Bulgaria and Georgia. This is of course logical, but it does not explain how these immigrant communities developed in the first place. A quite convincing argument, more than the first two, is that Romania, Bulgaria and Georgia had more flat land and thus fewer people were pushed from the land by land reform or farm consolidation than in the Balkans or Armenia. Although they possessed even more flat land than Romania, Bulgaria or Georgia, the more northerly Stalinist nations’ peoples established populations in the settler states during the <i>late nineteenth century</i>, which created opportunities for further immigration due to the existence of communities with familiar food and culture.<br /></p>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-12220013427407178322022-09-18T14:17:00.084+10:002022-10-11T23:35:21.381+11:00Workers in interwar Europe were likely more “deviant” than “media people” in 1990s AmericaIn <a href="http://jpbenney.blogspot.com/2022/09/hiding-basic-threat-against-which.html">my previous post</a>, I noted that it is likely that the threat posed by an activist working class to the Catholic Church was likely a very important driving factor behind stigmata stories in the southwestern quarter of Europe during the interwar period. This is true even if my original imagination — that the stigmata stories were designed to directly convert the workers — is unlikely to be true because the Church viewed converting the working classes as a fundamentally hopeless cause. The fact that the Church made few efforts other than by political power to do so suggests that no belief existed within the Catholic hierarchy that European workers could be converted from their fundamental anti-religion stance.<p>Indeed, the evidence I can gather reminds me of Peter Kreeft’s article <a href="https://www.peterkreeft.com/topics-more/culture-wars.htm">‘A Defense of Culture Wars’</a>, which I read as a young man in the late 1990s as part of his book <b><u>Ecumenical Jihad</u></b> to a mixture of utter ridicule and some agreement. Kreeft used a poll by the supposedly secular Wirthlin Agency — of whom I have not heard from <i>any</i> other source so I can doubt how secular it might have actually been — to illustrate differences in belief between the general population and “media people” (whom Kreeft defined as those involved in any of journalism, public education, or entertainment):</p><table class="tg">
<thead>
<tr>
<th class="tg-wa1i">Issue</th>
<th class="tg-wa1i" colspan="2">Support by general population</th>
<th class="tg-wa1i">Support by “media people”</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-cly1">Cheating sexually upon spouse is wrong</td>
<td class="tg-cly1" colspan="2">>90</td>
<td class="tg-cly1">50</td>
</tr>
<tr>
<td class="tg-cly1">Regular attendance at religious services</td>
<td class="tg-cly1" colspan="2">50</td>
<td class="tg-cly1">9</td>
</tr>
<tr>
<td class="tg-cly1" rowspan="2">Abortion should have minimally <span style="font-style: italic;">some</span> restrictions</td>
<td class="tg-cly1">72</td>
<td class="tg-cly1"><span style="font-style: normal; font-weight: 400; text-decoration: none;"> (Wirthlin)</span></td>
<td class="tg-cly1" rowspan="2">3</td>
</tr>
<tr>
<td class="tg-cly1">80</td>
<td class="tg-cly1"><span style="font-style: normal; font-weight: 400; text-decoration: none;">(other sources)</span></td>
</tr>
</tbody>
</table>The impression one obtains from church and other political histories, however, I have always envisioned as implying that the industrial working class of Europe between about 1860 and 1945 was even <i>more</i> “deviant” from the opinions and practices of the remainder of society. Pat Buchanan in his <b><u>The Death of the West</u></b> doubted this — indeed suggesting the working classes even in Europe were socially <i>conservative</i> — but he is unsupported by other sources. During periods of weak class struggle European workers accepted passively the system as it was, but when the gains mass class struggle could potentially produce were revealed, European workers always constituted the vanguard of social change.<div><br /></div><div>Almost certainly, the proportion of industrial workers in Europe over this period who attended religious services was extremely small, probably 5 percent or less. Contrariwise, amongst the ruling and middle classes, and the rural population, church attendance was typically very widespread (with some exceptions, for example the <b>latifundia</b> regions of interior Spain). From what I can gather, the proportion of all Europeans between 1860 and 1945 attending religious services was reasonably similar to 1990s America. This would mean Europe’s industrial working classes stood much further apart from the rest of society. Although abortion was not legalised outside the USSR and Scandinavia until the 1960s or 1970s, it is probable that the great majority of Europe‘s industrial workers had long supported eliminating restrictions upon it (and upon homosexual relations) since before the Bolshevik revolution.</div><div><br /></div><div>Moreover, if we extended the survey beyond sexual issues to economic ones, the views of media people in 1990s America would become less “deviant”, whereas those of workers in Europe between 1860 and 1945 would undoubtedly remain equally or more so. Additionally, because media people lack power to transform society — they have zero control either as bosses or producers over fundamental mechanisms of production — their deviant views and practices are extremely unlikely to transform society. Contrariwise, after World War Two the Boom Generation of Europeans (born after the war) confirmed in its social beliefs and practices to that which European workers had established within their own cultures as early as 1860, but was radically different to the remaining sectors of European society in this period.</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-44827611883124469592022-09-18T13:51:00.033+10:002022-10-10T23:47:33.475+11:00Hiding the basic threat against which stigmata stories were built<p>Today, as my brother and I repeated a familiar discussion about the origins of miracle stories like Thérèse Neumann and Marthe Robin, we made a now-unusual lapse into German on a slightly different note:</p><blockquote><p style="text-align: center;">“Es war eine politische Geschichte”<br />“Das stimmt nicht! Die Arbeiter war im großen und Ganzen nicht Kommunisten. Die Kirche wollte Sankte Thérèse!”</p></blockquote>The problem with what my brother says is that, whilst in ordinary circumstances German workers did not show overt sympathy or any evidence of support for revolutionary socialism, when other workers demonstrated what class struggle could achieve, German workers overwhelmingly supported revolutionary socialism because they saw that it was infinitely better for the majority than capitalism.<div><br /></div><div>It was this support that allowed the Bolshevik Government to survive against the intervention of 22 foreign armies. The threat of revolution at home compelled the ruling classes of Western and Central Europe to compromise. Part of the resulting compromise was withdrawing from Russia and not hosting a White Russian government-in-exile.<div><br /></div><div>When the stigmata stories of Thérèse Neumann (and Marthe Robin) were developed, the Catholic Church was living in fear of a workers’ revolution in Western Europe that would have expropriated the Church’s immense wealth, and left its priests and bishops under mortal threat of execution. The peasantry stood important in the success or failure of workers’ revolution. If the workers were able to give the peasants land by expropriating the big landowners (including the Church), they would support it, but if they failed to do this, the peasantry was very likely to support the Church. Given the uncompromising hostility between the Church and the workers, the peasantry was extremely critical in the battle for power.</div><div><br /></div><div>Even if it is unlikely any peasant shifted from the side of the workers to that of the Church upon observing supposed miracles, repeated exposure, like that to the struggles of workers on the other side, was bound to have effects. This would probably be true even for merely promoted miracles in the local area.</div></div><div><br /></div><div>In the case of the Fatima Marian apparition, there is no doubt of course that it was aimed at the threat of workers’ revolution expropriating the Church. As Portugal in 1917 had a much less developed working class than Germany or France, it is logical that the threat loomed even larger even if less explicit in these slightly later stigmata miracles.</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-72771172129768636472022-08-10T16:49:00.003+10:002022-08-13T14:12:42.261+10:00Serious, yet trivial in the big picture<p>A few days ago, I noticed discussion of how car companies have been trying to slow the shift towards electric vehicles, as has been discussed by <a href="https://www.smh.com.au/national/revealed-car-industry-s-secret-emissions-plan-would-slow-electric-vehicle-uptake-20220805-p5b7pe.html">Ben Cubby</a> in the <b><u>Sydney Morning Herald</u></b> a couple of days ago as I type this.</p><p>Especially since car manufacturing in Australia has been closed down after three decades of trying to stop it, car companies attract relatively little attention in the mind of the Australian public. Even in countries that still manufacture cars, car companies are rarely major newsmakers, despite their immense wealth and vast output. The Federal Chamber of Automotive Industries, even without any local car manufacturing, is nonetheless an immensely powerful lobby group inside Australia, representing thirty-nine makes of car. Despite the undoubted influence, even control, of the Federal Chamber of Automotive Industries upon Australian transport and energy policy, the organisation’s <i>name</i> is not known to most Australians.</p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZiKbptVfhLhtWn3ICaP762SF38gopS8UJEWiTiBdbBxFyMuBXS5exmYrufN86-Lg5JzRpYUOQjRN59MpdGfppxfHjJfUwYtk3Nzni_gXQoSTyKXKNRxIUqQvdSWk0pynNpOwpbS_KaRr4dGPDoQ8i_g_-B3qf0iAgJtwC7d6gRCzz6jF3zXlfSaV4/s589/Environment.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="589" data-original-width="420" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZiKbptVfhLhtWn3ICaP762SF38gopS8UJEWiTiBdbBxFyMuBXS5exmYrufN86-Lg5JzRpYUOQjRN59MpdGfppxfHjJfUwYtk3Nzni_gXQoSTyKXKNRxIUqQvdSWk0pynNpOwpbS_KaRr4dGPDoQ8i_g_-B3qf0iAgJtwC7d6gRCzz6jF3zXlfSaV4/s16000/Environment.jpg" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Despite being viewed by my relatives as propaganda, some quotes from <b><u>Environment, Capitalism and Socialism</u></b> continue to influence my thinking</td></tr></tbody></table><p>Ever since I read the pamphlets of the Public Transport Users Association, and much more so again after reading the now-defunct Democratic Socialist Party’s 1990 (updated 1999) book <b><u>Environment, Capitalism and Socialism</u></b>, I have come to believe that the production of private cars is <i><b>ipso facto</b> unsustainable and unnecessary</i>. That is to say, if <i>every last dollar of public and private money devoted to road building and car production were redirected to mass transit</i>, there would be large reductions in greenhouse gas emissions accompanied by zero loss of mobility for the majority of the population. The Public Transport Users Association — whom I came after reading the Trotskyists to regard as too lenient and compromising — nonetheless demonstrated in the early 1990s that a public transit system for Melbourne equal to the best in Europe and Japan would cost <i>one-twelfth</i> the amount actually wasted by the Kennett and other governments on the Scoresby, Mornington Peninsula, and Dingley Freeways, CityLink and the Western Ring Road. The evidence of the PTUA amply proved to me that the influence of the car industry must dictate transport policy in Australia, and that the most rational and logical policy would:</p><p></p><ul style="text-align: left;"><li>put an end to all trunk road building whatsoever</li><li>transfer all money spent on roads — excluding that spent upon their <i>demolition and revegetation</i> — to improvements in rail and other public transport</li><li>have as its ultimate goal a transport system based upon <i>100 percent public transit modal share</i> — initially in urban areas and subsequently elsewhere</li><li>aim to develop communities without local roads for private cars</li><ul><li>homes would be instead connected by single-lane roads for special uses or better still exclusively by footpaths or tramways</li></ul></ul><div>After I heard that cars were not the major single source of greenhouse gases during a holiday in the Otways in 2001, I slightly lessened insistence on the phase-out of private transport until reading Richard Smith’s <a href="https://www.ecologicalcitizen.net/pdfs/Vol%203%20Suppl%20B.pdf#%5B%7B%22num%22%3A3054%2C%22gen%22%3A0%7D%2C%7B%22name%22%3A%22FitR%22%7D%2C-330%2C316%2C925%2C912%5D">‘Elon Musk’s electric planet-suicide vehicle: Automobiles, emissions and degrowth’</a> last September.</div><div><br /></div><div>Smith’s article was published in Volume 3 Supplement B of the 2020 <b><u>Ecological Citizen</u></b>, and it suffices to say here that Smith demonstrated that to avoid catastrophic global warming:</div><div><ol style="text-align: left;"><li>the entire modern car industry must be shut down</li><li>vehicle production must be dramatically cut (by 99 percent or more) and all but the smallest vehicles banned from production entirely</li><li>there must be a complete transformation of the transport system to one based upon mass public transit for every journey</li></ol><div>What Smith, alongside the Democratic Socialist Party and Public Transport Users Association, does demonstrate is that road lobby groups like the Federal Chamber of Automotive Industries are a major factor in preventing urgently needed reductions in greenhouse gas emissions, and that <i>a strictly rational and logical transport system would have no place whatsoever for private motoring</i>. Unless the car companies who support groups like the Federal Chamber of Automotive Industries are completely nationalised and expropriated — and the resources and wealth they hold wholly redirected to the building of decades-overdue mass transit systems capable of <i>surpassing</i> the car in mobility — there can never be <i>any</i> reductions in greenhouse gas emissions.</div></div><div><br /></div><div>The best hope from this news is that people recognise the car companies and their front groups for what they are — ecological criminals for whom justice means expropriation of their entire wealth and assets and complete dismantling of the industries upon which this wealth is built. The public have undoubtedly been naïve about the car companies for far too long and a change in image is many decades overdue. The requisite image of the car companies is one of corporate polluters as bad as (possibly worse than) the less low-profile fossil fuel corporations.</div>jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0tag:blogger.com,1999:blog-7721656968238526975.post-87098636625910726142022-08-02T16:54:00.071+10:002022-08-02T17:21:11.713+10:00“In the abbess”!<p>Last month, as I have watched a little of the 1989 Ashes series for the first time (at least since it was played), I was more convinced than ever before that English bowling at the tail end of the 1980s really <i>was</i> worse than at any other time in the history of cricket.</p><p>The abysmal line and length of English bowlers throughout the series really confirms what the 1990 and 1991 <u><b>Wisden</b></u>s were saying about the inability of English bowlers of the time to master even the basics. It demonstrates beyond the smallest doubt that the “Year of the Bat” in the following 1990 season — when not a single England-qualified bowler bowling minimally 1,000 balls averaged under 26 and the average number of runs per wicket in county cricket rose to a whopping 38.72 — had <i>absolutely zilch</i> to do with the quality of the batting. The extraordinary scores of 1990 were due to a combination of</p><ol style="text-align: left;"><li>rigged pitches</li><ol><li>these were due to changes designed to reduce the effectiveness of county medium pacers, alongside full covering introduced to be more favourable to television broadcasting interests</li></ol><li>abysmal bowling standards as described above</li></ol><p>One amazing but funny mishearing occurred last month when I said English bowling in the late 1980s was</p><div style="text-align: center;"><blockquote>“in the <i>a</i>byss”</blockquote></div><p> was heard by my brother as</p><div style="text-align: center;"><blockquote>“in the <i>abbess</i>”!</blockquote></div>My brother even joked about an abbess being an English bowler — of course utterly ridiculous! Nonetheless, the joke still resonates with me because although “<u><i>a</i></u>-b<i>i</i>ss” is not the same sound as “<u><i>a</i></u>-b<i>e</i>ss”, the correct pronunciation of abyss is “a-<i>biss</i>”, as with acidic (which I very frequently mispronounced as “<i>a</i>-si-dic” when reading chemistry textbooks in school).<br />jpbenneyhttp://www.blogger.com/profile/02664829103165280260noreply@blogger.com0