Are prime-poor small centuries “expectedly” so?

On Mersenne Forum, there was a recent response to my previous blog post about moduli (3003), showing that not all centuries that are exceptionally poor in prime numbers have unusually few “potential” primes [“potential” primes being defined as numbers not divisible by 2, 3, 5, 7, 11, or 13 according to modulus (3003), with 3003 being the product of the first four primes coprime to 100].

In order to see whether centuries with abnormally few primes actually have few “potential” primes, I have aimed to test the modulus (3003) of every century up to ten million that has a record-low or equal-record-low number of primes (compared to smaller centuries only of course). These centuries, with their modulus (3003) and “potential” primes, are tabulated below

k	Total primes	mod (3003)	Total possible primes	...1	...3	...7	...9
2	16	2	17	5	5	3	4
3	16	3	19	4	5	6	4
5	14	5	18	4	4	5	5
7	14	7	19	4	5	4	6
9	14	9	18	6	3	6	3
11	12	11	17	4	5	3	5
13	11	13	18	4	5	5	4
21	10	21	15	4	5	3	3
24	10	24	18	4	3	6	5
31	10	31	20	6	4	5	5
41	9	41	17	4	4	5	4
43	9	43	21	4	5	6	6
48	8	48	19	7	4	5	3
59	7	59	19	3	6	5	5
95	7	95	18	4	5	5	4
142	7	142	20	4	5	5	6
165	7	165	18	5	3	5	5
167	7	167	19	5	3	5	6
186	6	186	17	5	3	5	4
188	5	188	17	3	4	5	5
273	5	273	20	6	5	5	4
314	4	314	17	3	5	4	5
356	4	356	19	5	4	6	4
524	4	524	18	4	4	6	4
588	3	588	19	5	5	4	5
695	3	695	17	5	4	4	4
797	3	797	16	4	3	5	4
1430	3	1430	17	5	5	3	4
1559	1	1559	17	4	5	4	4
2683	1	2683	20	5	4	4	7
4133	1	1130	17	5	6	3	3
10048	1	1039	20	5	6	5	4
11400	1	2391	18	5	3	5	5
12727	1	715	21	5	5	7	4
12800	1	788	19	3	6	5	5
13572	1	1560	21	6	4	6	5
14223	1	2211	19	6	4	4	5
14443	1	2431	19	5	3	6	5
14514	1	2502	16	3	4	5	4
14680	1	2668	21	5	5	6	5
14913	1	2901	19	4	4	6	5
15536	1	521	19	4	7	4	4
15619	1	604	20	5	4	4	7
16538	1	1523	17	4	6	3	4
16557	1	1542	18	5	4	5	4
16718	0	1703	20	6	6	3	5
26378	0	2354	17	5	5	3	4
31173	0	1143	17	4	4	5	4
39336	0	297	18	3	4	6	5
46406	0	1361	18	5	5	4	4
46524	0	1479	17	4	3	6	4
51782	0	731	17	4	6	3	4
55187	0	1133	16	3	4	4	5
58374	0	1317	20	5	6	6	3
58452	0	1395	19	6	4	6	3
60129	0	69	20	6	5	6	3
60850	0	790	19	5	5	4	5
63338	0	275	16	4	5	2	5
63762	0	699	19	5	4	6	4
67898	0	1832	17	3	5	4	5
69587	0	518	20	5	5	3	7
71299	0	2230	20	6	4	4	6
75652	0	577	20	5	5	5	5
78035	0	2960	20	4	5	5	6
78269	0	191	19	5	5	4	5
80277	0	2199	18	5	4	5	4
83674	0	2593	19	5	4	5	5
84213	0	129	19	3	5	6	5
89052	0	1965	19	6	4	4	5
95490	0	2397	17	5	4	5	3
97080	0	984	18	5	3	5	5

Results:

If we consider all centuries up to ten million that have an (equal) record low number of primes vis-à-vis preceding centuries, we find that:

“Potential primes”	All centuries	%	“Record few” centuries	%	Difference in %	Difference in ratio
15	4	0.13%	1	1.41%	1.28%	1057.39%
16	46	1.53%	4	5.63%	4.10%	367.79%
17	244	8.13%	17	23.94%	15.82%	294.68%
18	580	19.31%	13	18.31%	-1.00%	94.80%
19	954	31.77%	19	26.76%	-5.01%	84.24%
20	725	24.14%	13	18.31%	-5.83%	75.84%
21	336	11.19%	4	5.63%	-5.56%	50.35%
22	88	2.93%	0	0.00%	-2.93%	0.00%
23	26	0.87%	0	0.00%	-0.87%	0.00%

The table does seem to indicate systematic differences between centuries with the fewest primes up to that point, and all centuries, in terms of the number of potential primes. Whilst it is true that the proportion of moduli (3003) yielding 22 or 23 “potential primes” is very small, it is revealing that no century up to ten million with a record low number of primes has so many. With 19, 20 and 21 “potential primes”, the difference appears to be just as systematic inasmuch as the proportion of centuries with a record small number of primes having so many is consistently fewer than of all centuries. Contrariwise, for 15, 16 and 17 “potential primes”, the proportion is consistently higher for centuries with record few primes than for all centuries. This does imply that centuries with a record small number of primes do have a distinct tendency to have fewer “potential primes” than other centuries, even if the tendency is not consistent enough to apply to every such century.

Three strange fifteen-prime patterns

Looking through prime patterns today, I have come across two very interesting patterns for nine-digit fifteen-prime centuries, and one of six six-digit fifteen-prime centuries that has extraordinarily few possibilities to have so many:

“Full 9” 1,790,288^th Century:

179028701 = 71 × 277 × 9103

179028703 = 7 × 7 × 3653647

179028707 = 11 × 13 × 409 × 3061

1. 179028709 is prime [1.]

2. 179028713 is prime

3. 179028719 is prime [2.]

179028721 = 3373 × 53077

179028727 = 1699 × 105373

179028731 = 7 × 1163 × 21991

179028733 = 13 × 1451 × 9491

179028737 = 43 × 4163459

4. 179028739 is prime [3.]

5. 179028743 is prime

6. 179028749 is prime [4.]

179028751 = 11 × 17 × 31 × 89 × 347

179028757 = 23 × 67 × 116177

7. 179028761 is prime

8. 179028763 is prime

9. 179028767 is prime

10. 179028769 is prime [5.]

179028773 = 7 × 11 × 19 × 79 × 1549

11. 179028779 is prime [6.]

179028781 = 47 × 3809123

179028787 = 7 × 25575541 

12. 179028791 is prime

13. 179028793 is prime

14. 179028797 is prime

15. 179028799 is prime [7.]

Here we see a fifteen-prime century of the form 3k+1 with seven primes ending in 9 (a “full 9” century). The only smaller century with seven primes ending in 9 I know of is from 21,169,600 to 21,169,699, and it is not impossible that the 1,790,288^th century really is the second with seven primes ending in 9, though I have not asked about this yet.

What makes this pattern even stranger is that eight of the fifteen primes — six of the eight that do not end in 9 — are part of a pair of successive prime quadruples. The other two primes, both of which end in 3, also fit a remarkable pattern. In fact, except for 179,028,773, which has several small prime divisors and could be detected from the century’s modulus (231), there are only four decadal patterns for the whole century, each of which occurs multiple times. The only comparable pattern of which I am aware occurs in the fairly well-known 6,328^th century [632713, 632717, 632743, 632747, 632773, 632777]

The 2,527,250^th Century — 15 Primes, None Ending in 7:

252724901 = 11 × 13 × 1767307

1. 252724903 is prime [1.]

252724907 = 17 × 59 × 251969

252724909 = 19 × 19 × 179 × 3911

252724913 = 7 × 5197 × 6947

2. 252724919 is prime [1.]

3. 252724921 is prime [1.]

252724927 = 7 × 13 × 31 × 101 × 887

4. 252724931 is prime [2.]

5. 252724933 is prime [2.]

252724937 = 29 × 281 × 31013

6. 252724939 is prime [2.]

252724943 = 23 × 41 × 283 × 947

7. 252724949 is prime [3.]

8. 252724951 is prime [3.]

252724957 = 83 × 3044879

9. 252724961 is prime [4.]

10. 252724963 is prime [3.]

252724967 = 11 × 22974997

252724969 = 7 × 47 × 768161

11. 252724973 is prime [4.]

252724979 = 13 × 19440383

12. 252724981 is prime [5.]

252724987 = 1669 × 151423

13. 252724991 is prime [6.]

14. 252724993 is prime [5.]

252724997 = 7 × 7 × 71 × 72643

15. 252724999 is prime [4.]

What we see here is a fifteen-prime century with:

1. six primes ending in 1
2. five primes ending in 3
3. no prime ending in 7
4. four primes ending in 9

Although by deletion from several very small centuries with sixteen primes — the fourth and eleventh — one can easily draw up patterns with fourteen primes but no prime ending in one digit, this century with fifteen primes but not one ending in 7 surprised me so much I felt I had to tabulate it. What is strange here is that seven of thirteen composite numbers not divisible by 2, 3, or 5 end in 7.

The 1,573^rd Century — Almost All Potential Primes Prime

This century is much smaller than the previous two, and it is only today that I realised how improbable it was when one tests its numbers modulo not merely 3, but also 7, 11 and 13. Unlike the two larger centuries, I will tabulate all numbers not divisible by 2 or 5 to illustrate:

157201 = 11 × 31 × 461

157203 = 3 × 3 × 17467

1. 157207 is prime

157209 = 3 × 13 × 29 × 139

2. 157211 is prime

157213 = 7 × 37 × 607

3. 157217 is prime

4. 157219 is prime

157221 = 3 × 3 × 3 × 3 × 3 × 647

157223 = 11 × 14293

157227 = 3 × 7 × 7487

5. 157229 is prime

6. 157231 is prime

157233 = 3 × 17 × 3083

157237 = 97 × 1621

157239 = 3 × 3 × 17471

157241 = 7 × 7 × 3209

7. 157243 is prime

8. 157247 is prime

157249 = 67 × 2347

157251 = 3 × 23 × 43 × 53

9. 157253 is prime

157257 = 3 × 3 × 101 × 173

10. 157259 is prime

157261 = 13 × 12097

157263 = 3 × 19 × 31 × 89

157267 = 11 × 17 × 29 × 29

157269 = 3 × 7 × 7489

11. 157271 is prime

12. 157273 is prime

13. 157277 is prime

14. 157279 is prime

157281 = 3 × 103 × 509

157283 = 7 × 22469

157287 = 3 × 13 × 37 × 109

157289 = 11 × 79 × 181

15. 157291 is prime

157293 = 3 × 3 × 17477

157297 = 7 × 23 × 977

157299 = 3 × 52433

Here, we see that all but seventeen numbers, based on divisibility criteria, cannot be prime. Yet, of these seventeen, a remarkable fifteen actually are prime! Looking through tables modulo 21, 231 and finally 3003, I have never seen a case like this century. Despite the fact that nine numbers out of the 26 not divisible by 2, 3 or 5 can be ruled out modulo 7, 11 and/or 13, there are only two other composite numbers in the whole century. Although with centuries above the “eight-digit gap” I have seen this, in those cases all the composite numbers have highly complex factorisations, whereas 157,237 and 157,249 are semiprimes of a type familiar when learning early factorisations.

Centuries by modulo 13#/(2*5) and number of “potential primes”

Ever since I first studied primes, it has been obvious to me that some centuries can have more “potential primes” than others. Based upon simply divisibility by 2, 3, and 5, it is obvious that centuries 100k to 100k+99 can have two more primes if k is of the form 3n+1 than if k is of the forms 3n or 3n+2. However, in the past few years I have learned much more. Firstly, although centuries of the form 3k+1 have 28 numbers not divisible by 2, 3 or 5 — and other centuries have 26 such numbers — it is impossible for there to be 28 primes in 100 numbers, because some of these 28 numbers will always be divisible by 7, 11, or 13. In fact, I learned a few years back that 26 primes in 100 numbers is completely impossible, and that the maximum possible number is no more than 23. So far, no century greater than 200 with 21 or more primes is yet known, and although it is strongly believed they do exist, it is known that the smallest after 199 much be greater than 10²³.

One interesting thing when searching for such centuries is that, if one groups them by moduli of the product of larger primes coprime to 10, one can reduce the number of “potential primes” beyond the crude calculations based upon moduli 3. I have recently experimented with moduli 21 (3*7) and 231 (3*7*11) and found that the maximum possible number of primes can be reduced further below 26 or 28. However, the data are difficult to tabulate like one can for the crude modulo 3 calculations that I learned as a child. Today, I have tabulated centuries modulo 3003 (3*7*11*13) to see:

1. what variation exists among moduli
2. what patterns one can see in the variations noted in 1)
3. how the patterns compare with observed prime counts in small centuries
4. how may primes ending in each digit [1, 3, 7, 9] are theoretically possible for each modulo 3003

Prime Counts mod(3003) — total and for each final digit

mod 3003	Total possible p	...1	...3	...7	...9
0	20	5	5	5	5
1	21	5	5	6	5
2	17	5	5	3	4
3	19	4	5	6	4
4	19	5	4	4	6
5	18	4	4	5	5
6	19	5	5	6	3
7	19	4	5	4	6
8	20	5	5	5	5
9	18	6	3	6	3
10	21	6	6	4	5
11	17	4	5	3	5
12	21	5	4	6	6
13	18	4	5	5	4
14	20	4	6	4	6
15	19	6	5	5	3
16	21	4	5	6	6
17	18	4	5	4	5
18	19	6	4	4	5
19	20	5	5	5	5
20	20	4	5	5	6
21	15	4	5	3	3
22	23	6	6	7	4
23	19	5	5	3	6
24	18	4	3	6	5
25	19	6	5	4	4
26	20	3	6	6	5
27	19	6	3	5	5
28	19	5	4	5	5
29	19	4	6	4	5
30	19	5	5	5	4
31	20	6	4	5	5
32	18	4	4	5	5
33	21	5	5	5	6
34	18	5	5	4	4
35	20	5	4	5	6
36	18	4	5	6	3
37	21	5	5	4	7
38	17	5	6	3	3
39	19	4	4	6	5
40	22	6	6	5	5
41	17	4	4	5	4
42	20	6	5	5	4
43	21	4	5	6	6
44	18	5	5	3	5
45	19	4	5	6	4
46	20	6	5	4	5
47	19	2	5	6	6
48	19	7	4	5	3
49	18	3	6	5	4
50	18	5	4	3	6
51	20	5	5	5	5
52	19	5	4	6	4
53	20	5	6	3	6
54	18	5	3	5	5
55	21	6	5	6	4
56	19	4	5	4	6
57	17	5	5	4	3
58	21	6	4	5	6
59	19	3	6	5	5
60	18	4	4	5	5
61	22	6	6	5	5
62	18	4	4	5	5
63	19	5	5	4	5
64	20	6	5	5	4
65	19	6	5	4	4
66	19	4	5	5	5
67	19	6	4	4	5
68	19	3	6	5	5
69	20	6	5	6	3
70	20	4	4	6	6
71	18	5	4	4	5
72	18	4	5	5	4
73	20	5	6	4	5
74	19	5	4	4	6
75	20	5	4	6	5
76	19	4	6	4	5
77	18	4	5	4	5
78	19	5	4	6	4
79	20	6	4	5	5
80	18	3	6	4	5
81	18	6	3	4	5
82	23	5	6	6	6
83	18	4	4	5	5
84	18	5	6	4	3
85	20	5	4	6	5
86	20	5	6	3	6
87	18	5	4	6	3
88	20	6	5	5	4
89	18	3	5	4	6
90	19	5	4	5	5
91	20	5	5	6	4
92	19	5	6	4	4
93	19	5	4	5	5
94	20	5	5	5	5
95	18	4	5	5	4
96	19	5	5	4	5
97	20	6	4	5	5
98	19	4	4	5	6
99	18	4	6	4	4
100	21	5	4	6	6
101	19	5	6	4	4
102	20	5	4	6	5
103	19	4	6	4	5
104	19	5	4	5	5
105	19	5	5	4	5
106	20	4	5	6	5
107	18	5	6	2	5
108	20	5	4	7	4
109	20	6	5	3	6
110	17	4	4	5	4
111	20	6	4	5	5
112	19	4	6	5	4
113	20	5	4	5	6
114	17	5	4	5	3
115	21	4	6	6	5
116	18	4	5	4	5
117	19	5	4	5	5
118	19	5	4	6	4
119	20	5	6	3	6
120	18	5	5	4	4
121	21	5	4	6	6
122	18	4	6	4	4
123	17	4	3	5	5
124	22	6	5	6	5
125	20	4	5	6	5
126	18	5	4	4	5
127	20	5	5	6	4
128	19	5	5	3	6
129	19	3	5	6	5
130	20	6	6	4	4
131	18	4	5	5	4
132	19	6	4	4	5
133	20	4	5	5	6
134	18	5	4	5	4
135	19	5	5	5	4
136	19	5	4	4	6
137	19	5	5	4	5
138	19	5	5	5	4
139	21	5	6	6	4
140	18	5	4	3	6
141	18	5	4	6	3
142	20	4	5	5	6
143	18	4	6	4	4
144	20	6	3	5	6
145	19	4	6	5	4
146	19	4	4	5	6
147	20	6	5	5	4
148	23	6	6	6	5
149	16	4	4	3	5
150	18	4	5	5	4
151	21	6	5	5	5
152	20	4	5	5	6
153	19	6	4	5	4
154	19	4	5	5	5
155	20	5	6	4	5
156	18	5	3	5	5
157	21	6	5	6	4
158	17	3	6	4	4
159	19	5	4	4	6
160	19	5	5	5	4
161	20	4	5	5	6
162	19	4	6	5	4
163	19	6	3	4	6
164	20	5	6	5	4
165	18	5	3	5	5
166	19	4	6	4	5
167	19	5	3	5	6
168	19	4	6	5	4
169	19	4	4	6	5
170	19	6	5	4	4
171	19	5	4	6	4
172	21	5	6	4	6
173	18	4	5	5	4
174	20	7	4	5	4
175	20	4	6	4	6
176	18	4	5	4	5
177	18	5	4	5	4
178	20	5	6	5	4
179	20	5	4	5	6
180	18	5	3	5	5
181	20	5	6	5	4
182	19	4	5	4	6
183	18	6	5	4	3
184	20	4	5	6	5
185	20	4	7	4	5
186	17	5	3	5	4
187	22	6	6	5	5
188	17	3	4	5	5
189	17	4	5	3	5
190	23	6	5	6	6
191	19	5	5	4	5
192	17	4	3	6	4
193	20	6	5	4	5
194	19	4	6	5	4
195	20	6	4	5	5
196	18	5	4	5	4
197	20	5	5	5	5
198	20	5	5	5	5
199	20	4	5	5	6
200	18	5	4	5	4
201	19	5	5	5	4
202	20	6	5	4	5
203	19	4	5	4	6
204	19	5	5	6	3
205	19	4	5	4	6
206	18	5	5	4	4
207	20	5	4	6	5
208	22	4	6	6	6
209	16	4	4	4	4
210	19	6	4	4	5
211	21	4	6	6	5
212	18	4	5	4	5
213	19	5	4	6	4
214	20	6	5	4	5
215	18	2	5	5	6
216	19	6	5	5	3
217	21	5	5	6	5
218	20	6	5	3	6
219	17	5	3	5	4
220	20	5	5	5	5
221	19	4	6	4	5
222	19	5	4	4	6
223	18	5	4	6	3
224	21	4	6	5	6
225	19	6	5	5	3
226	19	6	3	4	6
227	17	3	6	5	3
228	19	5	4	4	6
229	20	6	6	4	4
230	21	5	5	6	5
231	18	4	5	5	4
232	20	4	5	5	6
233	20	6	5	4	5
234	18	3	4	7	4
235	20	6	4	4	6
236	17	3	5	4	5
237	20	6	5	5	4
238	20	4	5	5	6
239	20	6	5	5	4
240	17	5	4	5	3
241	22	6	5	5	6
242	17	3	5	4	5
243	20	6	3	6	5
244	19	4	6	4	5
245	20	4	5	4	7
246	19	6	5	5	3
247	20	4	4	6	6
248	18	5	6	3	4
249	18	6	3	4	5
250	21	4	6	6	5
251	18	4	4	5	5
252	17	5	5	4	3
253	22	6	5	6	5
254	19	4	5	4	6
255	18	4	4	6	4
256	21	7	5	5	4
257	19	3	6	5	5
258	19	5	4	5	5
259	18	4	5	4	5
260	20	5	6	5	4
261	19	5	4	5	5
262	20	5	4	6	5
263	18	4	5	4	5
264	21	6	5	5	5
265	18	5	4	4	5
266	19	4	5	5	5
267	20	5	6	5	4
268	20	5	5	4	6
269	18	5	5	4	4
270	17	4	3	6	4
271	22	5	7	4	6
272	18	5	4	4	5
273	20	6	5	5	4
274	21	5	5	6	5
275	16	4	5	2	5
276	21	5	5	6	5
277	20	5	5	5	5
278	18	3	4	6	5
279	18	6	4	5	3
280	19	4	5	5	5
281	20	5	5	4	6
282	19	6	4	5	4
283	19	5	5	5	4
284	21	5	6	4	6
285	19	4	4	6	5
286	18	5	4	6	3
287	20	5	6	3	6
288	18	5	4	5	4
289	21	5	4	6	6
290	19	3	6	5	5
291	18	5	4	4	5
292	20	6	5	4	5
293	19	3	5	6	5
294	18	5	6	3	4
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300	19	6	4	5	4
301	20	4	5	6	5
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462	19	4	6	4	5
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464	19	6	4	4	5
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474	20	6	4	5	5
475	20	5	6	4	5
476	21	3	6	5	7
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480	19	5	4	5	5
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485	19	4	6	4	5
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492	19	5	4	5	5
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494	19	5	5	5	4
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516	19	5	4	6	4
517	19	5	5	5	4
518	20	5	5	3	7
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628	21	5	5	5	6
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632	19	5	5	4	5
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655	20	7	4	4	5
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663	19	4	4	6	5
664	19	6	4	5	4
665	18	5	5	3	5
666	19	5	6	5	3
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710	20	5	6	4	5
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714	17	4	5	4	4
715	21	5	5	7	4
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722	19	4	5	5	5
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725	19	5	4	5	5
726	20	5	4	5	6
727	19	4	5	5	5
728	20	5	5	5	5
729	19	5	5	5	4
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731	17	4	6	3	4
732	19	5	4	6	4
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735	18	5	5	4	4
736	22	5	6	5	6
737	17	5	4	3	5
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740	18	3	5	5	5
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743	18	4	5	4	5
744	20	6	5	4	5
745	20	4	5	6	5
746	19	5	5	4	5
747	19	5	4	5	5
748	20	6	5	5	4
749	21	4	6	4	7
750	17	5	4	5	3
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753	20	5	4	5	6
754	20	5	5	5	5
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767	19	5	5	4	5
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780	17	4	3	6	4
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790	19	5	5	4	5
791	19	5	4	4	6
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793	19	4	3	6	6
794	18	5	6	4	3
795	19	6	3	5	5
796	22	5	6	5	6
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798	20	5	6	5	4
799	22	5	5	6	6
800	18	5	5	3	5
801	18	5	4	6	3
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804	20	6	3	6	5
805	18	3	6	4	5
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808	20	4	5	6	5
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812	20	4	6	4	6
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816	18	4	3	6	5
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818	20	5	5	5	5
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824	18	4	4	6	4
825	20	6	5	5	4
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827	20	5	5	5	5
828	18	5	4	6	3
829	19	5	5	4	5
830	19	5	6	3	5
831	20	4	5	6	5
832	19	4	5	6	4
833	19	5	5	3	6
834	19	6	4	6	3
835	21	4	5	5	7
836	17	3	5	4	5
837	19	6	3	5	5
838	20	5	6	4	5
839	20	4	4	6	6
840	17	5	5	4	3
841	23	6	6	7	4
842	18	5	4	3	6
843	18	4	4	6	4
844	19	5	5	4	5
845	21	4	6	5	6
846	18	6	4	4	4
847	20	5	4	6	5
848	19	4	6	3	6
849	19	6	4	5	4
850	20	6	4	5	5
851	17	3	5	5	4
852	19	4	4	5	6
853	19	6	6	4	3
854	20	4	5	5	6
855	18	4	5	6	3
856	21	6	4	5	6
857	18	5	6	4	3
858	19	4	4	5	6
859	21	5	6	5	5
860	18	4	4	5	5
861	20	5	6	5	4
862	20	4	4	6	6
863	19	6	4	4	5
864	18	4	5	6	3
865	20	6	5	3	6
866	18	3	5	5	5
867	21	7	4	6	4
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869	18	5	5	3	5
870	20	5	4	6	5
871	18	4	5	5	4
872	20	5	5	4	6
873	19	6	4	4	5
874	21	5	6	6	4
875	17	3	4	4	6
876	19	6	6	4	3
877	20	5	4	5	6
878	20	4	6	5	5
879	16	4	3	5	4
880	22	6	6	6	4
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882	18	5	4	4	5
883	22	6	5	6	5
884	19	5	6	4	4
885	19	4	4	6	5
886	19	6	4	5	4
887	19	3	6	5	5
888	20	6	5	5	4
889	19	5	4	5	5
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891	18	4	5	4	5
892	20	5	6	4	5
893	19	5	4	5	5
894	19	4	5	6	4
895	19	5	5	4	5
896	18	5	5	3	5
897	18	4	5	6	3
898	20	5	4	5	6
899	18	4	6	4	4
900	20	6	4	5	5
901	23	5	6	6	6
902	17	4	4	5	4
903	18	5	5	4	4
904	20	5	5	5	5
905	19	4	5	4	6
906	18	5	3	6	4
907	20	5	6	5	4
908	17	3	4	4	6
909	21	6	5	6	4
910	19	5	4	6	4
911	20	6	6	3	5
912	17	5	4	4	4
913	22	5	5	6	6
914	17	3	5	4	5
915	19	5	5	4	5
916	21	6	5	6	4
917	19	3	5	5	6
918	18	5	5	4	4
919	21	6	4	5	6
920	18	4	6	4	4
921	19	4	4	5	6
922	19	5	6	4	4
923	20	5	5	6	4
924	19	5	5	4	5
925	20	5	4	6	5
926	18	5	5	3	5
927	20	4	5	7	4
928	20	6	4	4	6
929	18	4	4	5	5
930	19	5	5	5	4
931	19	4	6	4	5
932	20	6	4	5	5
933	18	5	3	6	4
934	22	5	6	5	6
935	16	4	5	3	4
936	20	5	3	6	6
937	19	5	5	5	4
938	20	4	6	4	6
939	18	6	5	4	3
940	21	4	5	6	6
941	18	5	5	4	4
942	18	5	4	5	4
943	21	5	5	6	5
944	20	4	5	5	6
945	18	5	5	4	4
946	21	5	6	6	4
947	19	5	5	3	6
948	18	3	4	6	5
949	20	6	5	5	4
950	18	3	6	5	4
951	18	6	3	4	5
952	20	4	5	5	6
953	19	5	5	5	4
954	19	5	5	4	5
955	20	6	4	5	5
956	19	5	4	5	5
957	19	5	5	4	5
958	19	5	5	5	4
959	20	5	5	4	6
960	19	4	5	6	4
961	20	4	5	5	6
962	19	5	6	4	4
963	18	5	3	5	5
964	21	5	6	5	5
965	18	5	4	4	5
966	19	6	5	5	3
967	22	5	6	5	6
968	16	5	4	3	4
969	20	4	5	6	5
970	21	6	6	5	4
971	19	3	4	6	6
972	18	6	3	5	4
973	19	3	6	5	5
974	18	5	5	3	5
975	19	5	4	5	5
976	21	5	5	6	5
977	18	4	6	3	5
978	19	5	4	5	5
979	19	5	4	6	4
980	20	5	5	4	6
981	17	4	5	4	4
982	20	6	3	5	6
983	21	4	7	5	5
984	18	5	3	5	5
985	20	5	6	5	4
986	18	4	4	5	5
987	20	5	6	4	5
988	20	5	5	6	4
989	19	6	5	4	4
990	18	4	4	5	5
991	20	5	5	4	6
992	19	4	5	6	4
993	19	6	5	5	3
994	20	4	5	5	6
995	18	5	4	4	5
996	18	5	5	5	3
997	21	5	6	5	5
998	19	5	4	4	6
999	19	5	3	6	5
1000	19	4	6	4	5
1001	19	4	5	5	5
1002	20	6	5	5	4
1003	20	5	5	5	5
1004	18	3	6	4	5
1005	19	6	3	5	5
1006	22	5	6	5	6
1007	17	3	4	5	5
1008	18	5	6	3	4
1009	21	5	5	6	5
1010	20	6	5	3	6
1011	17	5	3	6	3
1012	20	6	5	4	5
1013	19	3	6	5	5
1014	18	5	3	5	5
1015	20	5	5	6	4
1016	19	4	6	5	4
1017	19	5	4	5	5
1018	19	5	4	5	5
1019	19	4	5	5	5
1020	19	5	5	4	5
1021	20	6	5	4	5
1022	20	4	5	5	6
1023	18	5	5	5	3
1024	19	4	4	5	6
1025	19	5	5	5	4
1026	20	5	4	6	5
1027	20	4	5	5	6
1028	18	5	4	5	4
1029	19	5	5	4	5
1030	22	4	6	6	6
1031	18	5	6	3	4
1032	18	5	4	6	3
1033	20	6	5	3	6
1034	17	3	4	5	5
1035	19	6	4	5	4
1036	20	4	6	5	5
1037	19	5	4	4	6
1038	19	6	4	5	4
1039	20	5	6	5	4
1040	19	4	5	5	5
1041	19	6	4	4	5
1042	17	4	4	6	3
1043	21	4	6	4	7
1044	18	5	5	5	3
1045	21	6	4	5	6
1046	17	3	6	4	4
1047	19	5	3	5	6
1048	22	6	6	5	5
1049	21	5	5	6	5
1050	16	4	4	4	4
1051	20	5	5	5	5
1052	20	5	6	4	5
1053	19	4	4	6	5
1054	21	7	5	4	5
1055	17	3	5	5	4
1056	21	6	5	5	5
1057	19	4	4	5	6
1058	20	6	5	5	4
1059	17	4	5	5	3
1060	19	5	4	4	6
1061	19	4	6	4	5
1062	20	5	4	6	5
1063	20	4	6	5	5
1064	18	5	4	3	6
1065	20	6	5	6	3
1066	19	4	4	5	6
1067	17	4	6	3	4
1068	19	6	2	5	6
1069	21	4	7	5	5
1070	17	3	3	6	5
1071	19	6	5	5	3
1072	22	6	5	6	5
1073	18	4	5	3	6
1074	18	5	5	5	3
1075	21	6	5	5	5
1076	20	4	6	4	6
1077	18	5	4	5	4
1078	18	4	5	5	4
1079	20	5	6	4	5
1080	19	6	3	5	5
1081	20	5	4	6	5
1082	19	4	6	4	5
1083	19	5	4	5	5
1084	19	6	5	4	4
1085	19	3	6	5	5
1086	19	4	6	5	4
1087	19	6	4	4	5
1088	20	5	6	5	4
1089	17	4	3	5	5
1090	20	4	6	4	6
1091	20	5	4	5	6
1092	19	5	5	5	4
1093	20	5	4	6	5
1094	17	5	5	3	4
1095	20	5	5	6	4
1096	21	6	5	4	6
1097	17	4	4	5	4
1098	20	6	4	6	4
1099	20	4	5	5	6
1100	19	4	6	4	5
1101	19	6	3	6	4
1102	19	5	6	4	4
1103	20	5	5	4	6
1104	19	5	4	5	5
1105	19	4	5	6	4
1106	18	4	5	3	6
1107	19	6	5	5	3
1108	21	4	5	6	6
1109	20	4	6	5	5
1110	16	5	3	4	4
1111	21	6	5	5	5
1112	19	3	5	5	6
1113	17	4	5	4	4
1114	23	6	5	7	5
1115	18	5	5	3	5
1116	18	3	4	6	5
1117	19	6	5	4	4
1118	21	4	6	6	5
1119	19	6	4	4	5
1120	18	5	4	5	4
1121	20	5	5	4	6
1122	19	5	5	5	4
1123	20	5	5	4	6
1124	17	4	4	5	4
1125	21	5	5	6	5
1126	19	6	5	4	4
1127	19	5	4	4	6
1128	17	4	5	6	2
1129	21	5	5	4	7
1130	17	5	6	3	3
1131	20	5	4	6	5
1132	22	5	6	6	5
1133	16	3	4	4	5
1134	21	6	5	5	5
1135	20	4	5	6	5
1136	19	5	4	4	6
1137	17	4	4	5	4
1138	20	6	5	4	5
1139	19	3	5	5	6
1140	21	7	5	6	3
1141	18	4	5	5	4
1142	21	6	5	4	6
1143	17	4	4	5	4
1144	20	5	4	6	5
1145	19	4	6	3	6
1146	19	5	4	4	6
1147	21	6	5	6	4
1148	19	3	5	5	6
1149	18	6	5	4	3
1150	19	6	3	4	6
1151	18	3	6	5	4
1152	18	4	4	5	5
1153	21	6	6	5	4
1154	19	5	4	5	5
1155	19	4	5	5	5
1156	21	5	5	6	5
1157	19	6	5	4	4
1158	19	4	5	6	4
1159	19	5	5	4	5
1160	18	3	5	4	6
1161	20	6	5	6	3
1162	20	4	5	5	6
1163	19	5	4	5	5
1164	18	5	4	5	4
1165	21	6	6	4	5
1166	17	4	4	4	5
1167	20	5	4	6	5
1168	20	5	6	4	5
1169	20	4	6	4	6
1170	17	5	4	5	3
1171	20	5	4	6	5
1172	18	4	6	3	5
1173	19	6	4	4	5
1174	22	5	6	6	5
1175	19	5	4	5	5
1176	16	4	5	3	4
1177	22	6	5	6	5
1178	20	4	6	4	6
1179	17	4	3	6	4
1180	20	6	5	5	4
1181	18	3	5	5	5
1182	20	6	4	5	5
1183	19	5	4	5	5
1184	19	5	6	4	4
1185	20	5	5	5	5
1186	21	5	5	6	5
1187	17	4	4	5	4
1188	20	6	5	4	5
1189	19	5	4	5	5
1190	19	4	4	5	6
1191	19	4	6	5	4
1192	21	5	5	5	6
1193	17	5	5	3	4
1194	19	4	4	6	5
1195	21	5	7	4	5
1196	18	5	4	5	4
1197	18	6	4	4	4
1198	20	4	5	6	5
1199	17	4	5	3	5
1200	22	5	5	7	5
1201	20	6	5	4	5
1202	19	3	5	6	5
1203	18	6	4	4	4
1204	19	4	6	5	4
1205	19	5	4	4	6
1206	18	5	4	5	4
1207	20	4	5	6	5
1208	19	5	6	3	5
1209	18	4	3	6	5
1210	19	6	4	6	3
1211	20	5	6	3	6
1212	18	5	5	4	4
1213	21	5	4	6	6
1214	19	4	6	5	4
1215	17	4	4	4	5
1216	22	6	6	5	5
1217	19	3	5	6	5
1218	20	6	5	4	5
1219	20	5	5	5	5
1220	18	6	4	3	5
1221	19	3	5	6	5
1222	19	5	5	4	5
1223	19	4	6	5	4
1224	19	6	4	5	4
1225	21	4	5	6	6
1226	17	5	4	4	4
1227	19	5	5	5	4
1228	21	5	5	5	6
1229	19	5	4	4	6
1230	18	5	4	5	4
1231	20	5	6	5	4
1232	18	4	4	4	6
1233	19	5	4	6	4
1234	21	5	5	5	6
1235	19	4	6	5	4
1236	17	6	2	4	5
1237	21	4	6	6	5
1238	19	4	5	4	6
1239	19	6	6	4	3
1240	21	5	5	6	5
1241	18	5	5	3	5
1242	18	4	4	6	4
1243	21	7	5	5	4
1244	19	3	5	5	6
1245	19	5	4	5	5
1246	20	4	6	5	5
1247	19	5	6	4	4
1248	18	4	3	6	5
1249	20	6	5	5	4
1250	17	3	6	4	4
1251	20	5	5	4	6
1252	19	5	4	5	5
1253	19	5	4	5	5
1254	19	5	6	4	4
1255	20	5	3	5	7
1256	20	5	6	5	4
1257	19	6	3	6	4
1258	19	4	6	4	5
1259	18	5	4	4	5
1260	20	4	6	5	5
1261	20	4	5	6	5
1262	20	6	6	3	5
1263	18	5	3	6	4
1264	21	5	6	4	6
1265	17	4	4	5	4
1266	20	7	4	5	4
1267	19	4	6	4	5
1268	20	5	4	5	6
1269	17	5	5	4	3
1270	21	5	6	6	4
1271	19	4	4	5	6
1272	19	5	4	5	5
1273	18	4	5	5	4
1274	21	5	6	4	6
1275	17	5	4	4	4
1276	21	5	4	6	6
1277	18	3	7	3	5
1278	19	5	3	6	5
1279	21	6	5	5	5
1280	18	4	4	6	4
1281	17	4	5	3	5
1282	21	6	5	5	5
1283	20	5	5	4	6
1284	18	4	4	6	4
1285	21	6	6	4	5
1286	18	4	5	5	4
1287	19	5	4	5	5
1288	20	5	5	5	5
1289	19	5	5	5	4
1290	19	5	5	5	4
1291	19	4	4	5	6
1292	18	5	5	4	4
1293	19	5	5	5	4
1294	21	5	6	5	5
1295	19	4	5	4	6
1296	18	6	4	6	2
1297	20	5	5	4	6
1298	18	4	5	4	5
1299	20	5	3	6	6
1300	20	4	6	5	5
1301	18	4	4	5	5
1302	19	6	5	4	4
1303	23	5	6	7	5
1304	17	4	5	3	5
1305	19	5	5	5	4
1306	20	6	4	4	6
1307	19	3	5	5	6
1308	17	5	5	4	3
1309	21	5	5	6	5
1310	19	5	5	3	6
1311	19	6	3	5	5
1312	19	5	5	5	4
1313	19	4	6	5	4
1314	19	5	3	5	6
1315	18	5	5	5	3
1316	20	3	6	5	6
1317	20	5	6	6	3
1318	19	6	3	4	6
1319	18	4	5	5	4
1320	19	5	4	4	6
1321	20	5	6	4	5
1322	21	5	4	6	6
1323	17	4	5	5	3
1324	20	4	5	5	6
1325	19	6	5	4	4
1326	19	4	4	7	4
1327	21	6	5	4	6
1328	17	3	5	5	4
1329	21	7	4	5	5
1330	19	3	5	5	6
1331	19	5	6	4	4
1332	18	5	4	5	4
1333	19	5	5	4	5
1334	20	4	5	5	6
1335	18	6	3	5	4
1336	19	4	6	5	4
1337	18	4	4	3	7
1338	20	6	6	5	3
1339	20	5	4	6	5
1340	20	5	7	4	4
1341	16	5	2	4	5
1342	22	5	6	6	5
1343	17	3	4	5	5
1344	18	5	5	4	4
1345	23	6	5	6	6
1346	18	4	5	4	5
1347	17	4	4	5	4
1348	22	7	5	5	5
1349	20	4	6	5	5
1350	19	5	4	5	5
1351	17	4	5	4	4
1352	21	6	5	5	5
1353	19	5	4	5	5
1354	21	5	5	5	6
1355	18	4	5	4	5
1356	20	5	5	6	4
1357	20	6	4	5	5
1358	18	4	5	4	5
1359	18	4	6	5	3
1360	20	5	5	4	6
1361	18	5	5	4	4
1362	19	5	3	6	5
1363	22	4	7	5	6
1364	17	4	4	4	5
1365	20	6	4	5	5
1366	20	5	5	6	4
1367	17	4	5	3	5
1368	19	5	4	5	5
1369	20	5	5	5	5
1370	17	3	4	5	5
1371	20	6	5	6	3
1372	19	5	4	5	5
1373	21	5	6	4	6
1374	17	5	4	5	3
1375	21	6	5	5	5
1376	19	4	6	3	6
1377	20	4	5	5	6
1378	18	5	4	6	3
1379	19	4	6	4	5
1380	19	6	4	5	4
1381	20	5	4	5	6
1382	19	4	6	5	4
1383	18	5	4	4	5
1384	20	6	5	4	5
1385	20	4	5	6	5
1386	18	4	6	4	4
1387	21	5	5	6	5
1388	19	6	5	3	5
1389	18	3	4	7	4
1390	18	5	5	3	5
1391	20	4	5	5	6
1392	19	6	4	5	4
1393	19	4	5	5	5
1394	19	5	5	4	5
1395	19	6	4	6	3
1396	21	6	5	4	6
1397	16	4	4	4	4
1398	21	5	4	6	6
1399	20	5	6	5	4
1400	21	4	5	5	7
1401	16	5	4	5	2
1402	21	5	5	5	6
1403	18	5	6	3	4
1404	19	5	4	5	5
1405	21	5	5	6	5
1406	18	4	5	4	5
1407	18	5	5	4	4
1408	22	5	5	7	5
1409	20	5	5	4	6
1410	16	3	4	5	4
1411	20	7	4	4	5
1412	19	2	6	6	5
1413	19	6	4	5	4
1414	19	4	5	5	5
1415	19	5	5	4	5
1416	19	4	5	5	5
1417	20	5	5	6	4
1418	19	5	5	4	5
1419	20	6	4	4	6
1420	20	5	5	5	5
1421	18	4	4	5	5
1422	19	5	6	5	3
1423	20	5	4	4	7
1424	17	4	5	4	4
1425	19	5	4	6	4
1426	23	6	7	5	5
1427	17	5	3	4	5
1428	18	5	4	5	4
1429	21	5	6	5	5
1430	17	5	5	3	4
1431	21	5	5	6	5
1432	19	5	5	5	4
1433	18	2	5	5	6
1434	20	7	4	5	4
1435	20	4	5	6	5
1436	18	4	4	4	6
1437	19	5	5	4	5
1438	19	5	5	5	4
1439	20	5	5	4	6
1440	19	5	4	6	4
1441	19	5	5	5	4
1442	21	5	6	4	6
1443	17	4	4	5	4
1444	20	6	3	6	5
1445	19	3	7	4	5
1446	19	5	4	4	6
1447	21	6	5	5	5
1448	19	4	4	6	5
1449	18	5	6	3	4
1450	20	6	4	5	5
1451	19	5	5	4	5
1452	18	4	4	6	4
1453	19	5	5	4	5
1454	19	4	5	5	5
1455	20	5	5	6	4
1456	19	4	4	6	5
1457	19	6	5	4	4
1458	19	5	5	5	4
1459	21	4	6	5	6
1460	18	4	5	4	5
1461	19	6	4	5	4
1462	20	5	5	5	5
1463	18	3	4	5	6
1464	19	5	5	5	4
1465	21	6	5	5	5
1466	18	4	5	4	5
1467	18	5	3	5	5
1468	22	5	7	5	5
1469	19	4	5	5	5
1470	18	6	5	3	4
1471	19	4	4	7	4
1472	19	5	6	2	6
1473	19	5	4	6	4
1474	21	7	5	4	5
1475	18	3	5	5	5
1476	18	5	4	4	5
1477	21	5	6	5	5
1478	20	5	5	5	5
1479	17	4	3	6	4
1480	20	5	5	5	5
1481	18	4	6	4	4
1482	20	5	4	5	6
1483	19	6	4	5	4
1484	19	5	5	4	5
1485	20	5	6	5	4
1486	21	4	4	6	7
1487	18	5	5	5	3
1488	18	5	4	5	4
1489	21	5	5	5	6
1490	18	4	4	5	5
1491	20	5	5	5	5
1492	20	4	6	5	5
1493	18	6	5	2	5
1494	19	4	4	7	4
1495	20	5	6	4	5
1496	17	4	5	4	4
1497	20	7	3	5	5
1498	19	3	6	5	5
1499	18	4	4	5	5
1500	20	6	5	5	4
1501	20	5	5	5	5
1502	20	4	5	5	6
1503	18	5	5	4	4
1504	19	5	5	6	3
1505	20	5	5	3	7
1506	17	4	4	5	4
1507	20	5	4	6	5
1508	19	4	7	4	4
1509	18	5	2	5	6
1510	20	5	5	6	4
1511	20	5	5	5	5
1512	18	5	5	4	4
1513	21	6	5	5	5
1514	18	4	5	4	5
1515	18	3	5	5	5
1516	21	7	6	4	4
1517	20	4	5	6	5
1518	19	5	4	5	5
1519	19	4	5	4	6
1520	20	6	5	4	5
1521	18	4	4	6	4
1522	20	5	5	5	5
1523	17	4	6	3	4
1524	20	5	5	5	5
1525	21	5	5	6	5
1526	18	5	4	4	5
1527	18	5	5	5	3
1528	21	5	4	5	7
1529	19	4	6	4	5
1530	19	6	2	6	5
1531	19	4	7	4	4
1532	18	4	3	5	6
1533	19	5	5	5	4
1534	22	5	5	7	5
1535	18	5	5	3	5
1536	18	5	4	5	4
1537	21	5	5	5	6
1538	19	4	5	5	5
1539	18	6	5	4	3
1540	20	5	5	5	5
1541	19	4	5	4	6
1542	18	5	4	5	4
1543	21	6	5	6	4
1544	19	4	5	5	5
1545	19	4	4	5	6
1546	19	5	6	4	4
1547	20	4	6	5	5
1548	19	5	5	5	4
1549	19	5	4	5	5
1550	18	4	6	4	4
1551	19	5	4	5	5
1552	20	5	5	4	6
1553	18	4	3	6	5
1554	19	5	6	4	4
1555	21	5	5	5	6
1556	19	6	4	4	5
1557	19	5	4	7	3
1558	20	5	6	3	6
1559	17	4	5	4	4
1560	21	6	4	6	5
1561	19	4	5	5	5
1562	19	4	6	4	5
1563	20	6	4	5	5
1564	19	4	5	5	5
1565	19	5	4	5	5
1566	18	6	4	4	4
1567	20	5	6	5	4
1568	20	4	5	4	7
1569	18	6	5	5	2
1570	19	4	5	5	5
1571	21	5	6	5	5
1572	17	4	3	5	5
1573	21	5	5	6	5
1574	18	4	5	4	5
1575	17	5	4	3	5
1576	23	5	5	7	6
1577	19	4	6	4	5
1578	17	4	4	5	4
1579	20	7	4	4	5
1580	19	3	5	6	5
1581	18	5	5	4	4
1582	20	5	5	5	5
1583	20	6	4	4	6
1584	19	5	4	5	5
1585	20	4	6	5	5
1586	19	5	5	5	4
1587	19	5	4	5	5
1588	19	5	5	5	4
1589	19	4	5	4	6
1590	19	5	6	6	2
1591	20	5	4	4	7
1592	16	4	5	4	3
1593	20	6	4	5	5
1594	22	5	7	5	5
1595	18	4	4	5	5
1596	18	5	4	5	4
1597	21	5	6	5	5
1598	19	5	5	4	5
1599	18	4	3	6	5
1600	21	6	5	5	5
1601	16	2	5	4	5
1602	21	7	5	5	4
1603	20	4	5	6	5
1604	21	6	6	4	5
1605	16	4	4	4	4
1606	21	6	4	5	6
1607	19	3	6	4	6
1608	19	5	4	5	5
1609	19	5	5	5	4
1610	19	4	5	4	6
1611	20	6	5	5	4
1612	18	5	3	5	5
1613	18	4	7	4	3
1614	19	5	3	5	6
1615	21	5	6	5	5
1616	18	4	4	6	4
1617	20	5	6	5	4
1618	20	5	4	5	6
1619	18	5	4	4	5
1620	19	4	5	6	4
1621	20	6	5	4	5
1622	19	4	5	4	6
1623	19	5	4	6	4
1624	18	3	6	4	5
1625	20	6	5	5	4
1626	19	6	3	6	4
1627	21	5	5	5	6
1628	17	3	5	4	5
1629	21	6	4	6	5
1630	19	5	5	4	5
1631	20	3	6	5	6
1632	17	5	5	4	3
1633	20	5	5	5	5
1634	19	5	5	4	5
1635	17	5	3	5	4
1636	20	4	6	5	5
1637	20	5	5	4	6
1638	17	5	4	4	4
1639	22	6	5	7	4
1640	19	5	6	3	5
1641	18	4	4	5	5
1642	20	6	4	5	5
1643	18	3	5	6	4
1644	18	5	4	5	4
1645	20	5	5	4	6
1646	20	4	6	5	5
1647	18	5	4	5	4
1648	21	6	5	5	5
1649	19	5	5	4	5
1650	21	5	5	5	6
1651	17	4	4	5	4
1652	19	5	5	4	5
1653	20	5	5	6	4
1654	22	5	5	5	7
1655	17	4	5	4	4
1656	18	5	4	5	4
1657	23	6	6	5	6
1658	18	4	4	5	5
1659	17	5	5	4	3
1660	22	5	6	6	5
1661	16	5	4	2	5
1662	20	4	4	7	5
1663	20	5	6	4	5
1664	20	3	5	6	6
1665	18	7	3	4	4
1666	19	4	5	6	4
1667	18	4	5	3	6
1668	20	6	5	5	4
1669	19	5	4	5	5
1670	18	4	5	4	5
1671	19	4	4	6	5
1672	19	6	5	5	3
1673	21	5	5	4	7
1674	17	4	5	5	3
1675	21	6	4	5	6
1676	19	4	7	4	4
1677	19	4	4	5	6
1678	20	6	5	5	4
1679	17	3	5	5	4
1680	21	6	6	4	5
1681	20	5	4	6	5
1682	19	6	4	4	5
1683	18	4	5	5	4
1684	19	6	4	3	6
1685	20	3	6	6	5
1686	20	6	5	6	3
1687	18	3	5	5	5
1688	19	6	5	3	5
1689	19	4	5	6	4
1690	19	4	5	5	5
1691	19	5	5	3	6
1692	19	6	3	5	5
1693	21	5	6	5	5
1694	17	3	4	5	5
1695	19	6	5	5	3
1696	20	6	4	4	6
1697	19	4	5	5	5
1698	17	5	3	5	4
1699	23	5	7	6	5
1700	19	4	4	5	6
1701	18	5	5	4	4
1702	20	5	5	6	4
1703	20	6	6	3	5
1704	18	5	4	5	4
1705	20	6	4	5	5
1706	18	2	6	4	6
1707	19	6	4	5	4
1708	21	5	5	6	5
1709	19	4	5	5	5
1710	18	4	4	5	5
1711	19	6	5	4	4
1712	19	4	5	5	5
1713	19	4	5	5	5
1714	20	5	5	5	5
1715	19	5	5	4	5
1716	18	4	5	5	4
1717	21	5	4	6	6
1718	18	4	6	4	4
1719	20	6	4	5	5
1720	21	5	5	5	6
1721	17	5	3	5	4
1722	18	4	6	4	4
1723	21	5	5	5	6
1724	19	5	6	3	5
1725	18	5	3	7	3
1726	21	6	6	4	5
1727	17	4	4	4	5
1728	21	6	4	6	5
1729	18	4	5	5	4
1730	19	5	5	4	5
1731	19	6	5	4	4
1732	21	4	6	6	5
1733	17	3	4	5	5
1734	20	6	5	4	5
1735	19	5	4	6	4
1736	20	4	5	4	7
1737	17	4	5	4	4
1738	21	6	4	6	5
1739	18	4	6	3	5
1740	20	5	3	6	6
1741	20	5	6	5	4
1742	20	5	5	6	4
1743	18	5	4	4	5
1744	19	5	4	6	4
1745	19	4	6	3	6
1746	20	4	5	6	5
1747	20	7	5	3	5
1748	19	4	4	6	5
1749	19	5	5	4	5
1750	19	5	5	4	5
1751	20	6	4	5	5
1752	17	4	4	6	3
1753	20	4	5	5	6
1754	18	5	6	3	4
1755	19	4	4	6	5
1756	20	5	5	6	4
1757	19	5	5	4	5
1758	19	6	5	5	3
1759	21	4	5	5	7
1760	18	4	6	4	4
1761	18	5	3	5	5
1762	21	5	6	5	5
1763	19	3	4	6	6
1764	19	6	4	5	4
1765	21	5	6	6	4
1766	17	5	4	2	6
1767	19	4	5	6	4
1768	21	6	5	5	5
1769	19	4	6	4	5
1770	18	6	4	4	4
1771	20	4	5	6	5
1772	18	4	5	4	5
1773	19	6	4	4	5
1774	21	6	5	5	5
1775	19	4	5	5	5
1776	17	4	4	4	5
1777	21	6	6	5	4
1778	19	4	5	4	6
1779	19	4	5	6	4
1780	19	5	4	5	5
1781	19	5	6	5	3
1782	18	5	3	4	6
1783	20	5	5	5	5
1784	20	5	4	5	6
1785	19	5	6	5	3
1786	22	5	5	6	6
1787	17	5	4	4	4
1788	19	4	5	6	4
1789	21	6	6	4	5
1790	18	4	4	5	5
1791	20	6	3	6	5
1792	19	3	6	4	6
1793	18	5	6	3	4
1794	19	5	3	6	5
1795	20	5	6	5	4
1796	18	4	5	4	5
1797	19	6	4	4	5
1798	19	4	5	6	4
1799	18	4	4	4	6
1800	19	5	6	5	3
1801	20	5	4	5	6
1802	22	5	7	5	5
1803	17	5	3	5	4
1804	20	5	6	5	4
1805	18	4	4	4	6
1806	18	4	5	4	5
1807	21	5	4	7	5
1808	19	5	6	4	4
1809	17	4	3	5	5
1810	21	6	5	5	5
1811	19	4	5	6	4
1812	19	6	5	4	4
1813	19	5	5	4	5
1814	20	5	4	5	6
1815	17	4	5	4	4
1816	21	5	6	5	5
1817	20	5	5	5	5
1818	19	4	4	6	5
1819	19	5	5	4	5
1820	20	5	5	4	6
1821	18	5	5	5	3
1822	20	4	5	5	6
1823	17	4	6	3	4
1824	20	6	4	6	4
1825	22	5	6	5	6
1826	16	4	3	5	4
1827	19	5	5	4	5
1828	22	5	6	6	5
1829	19	5	4	4	6
1830	18	5	3	6	4
1831	20	5	6	4	5
1832	17	3	5	4	5
1833	20	6	4	6	4
1834	20	5	4	6	5
1835	20	5	6	4	5
1836	17	5	4	4	4
1837	21	5	4	6	6
1838	18	4	5	4	5
1839	19	5	5	4	5
1840	20	6	5	5	4
1841	20	3	6	5	6
1842	18	6	4	5	3
1843	19	5	4	5	5
1844	19	4	6	5	4
1845	19	4	4	5	6
1846	21	5	6	5	5
1847	19	5	5	5	4
1848	19	5	5	4	5
1849	21	4	5	6	6
1850	18	5	5	4	4
1851	18	4	5	6	3
1852	19	6	4	3	6
1853	18	3	4	5	6
1854	19	6	5	5	3
1855	21	4	6	5	6
1856	19	6	4	4	5
1857	19	6	3	6	4
1858	20	5	6	4	5
1859	17	4	5	4	4
1860	21	6	4	5	6
1861	18	4	5	5	4
1862	21	3	6	5	7
1863	19	6	5	5	3
1864	20	5	4	5	6
1865	17	4	5	4	4
1866	19	6	4	4	5
1867	20	5	6	5	4
1868	21	5	5	5	6
1869	16	5	4	4	3
1870	22	5	6	6	5
1871	20	5	6	4	5
1872	17	3	3	6	5
1873	21	7	4	5	5
1874	17	2	6	5	4
1875	19	6	4	4	5
1876	19	4	4	5	6
1877	21	5	6	5	5
1878	17	4	5	4	4
1879	20	6	4	5	5
1880	19	4	5	5	5
1881	20	6	4	5	5
1882	18	4	5	4	5
1883	19	5	4	4	6
1884	21	5	6	6	4
1885	19	4	4	5	6
1886	18	5	6	4	3
1887	18	5	3	5	5
1888	23	5	7	5	6
1889	17	4	4	5	4
1890	19	6	5	5	3
1891	21	5	5	5	6
1892	16	4	4	3	5
1893	20	5	5	6	4
1894	21	6	6	5	4
1895	19	3	5	5	6
1896	18	6	3	5	4
1897	19	4	6	5	4
1898	19	5	5	4	5
1899	20	6	4	5	5
1900	19	4	4	6	5
1901	19	4	6	3	6
1902	19	5	4	6	4
1903	20	6	5	5	4
1904	20	4	6	4	6
1905	17	4	5	4	4
1906	21	6	4	5	6
1907	20	4	6	5	5
1908	17	4	3	5	5
1909	20	5	6	4	5
1910	19	4	5	5	5
1911	20	6	5	4	5
1912	20	6	4	6	4
1913	17	5	5	3	4
1914	20	4	5	6	5
1915	19	5	4	4	6
1916	19	4	5	6	4
1917	19	5	5	6	3
1918	19	4	4	5	6
1919	19	5	5	4	5
1920	19	5	4	6	4
1921	20	5	6	4	5
1922	19	5	5	3	6
1923	20	5	4	6	5
1924	18	4	5	5	4
1925	18	4	5	4	5
1926	20	6	4	6	4
1927	21	5	5	5	6
1928	18	3	5	5	5
1929	18	6	3	5	4
1930	22	5	6	5	6
1931	19	3	5	5	6
1932	17	5	6	3	3
1933	21	5	5	7	4
1934	19	6	5	2	6
1935	17	4	3	6	4
1936	19	6	5	4	4
1937	20	3	6	5	6
1938	18	6	3	4	5
1939	20	5	5	6	4
1940	20	5	6	4	5
1941	19	5	4	6	4
1942	19	6	4	4	5
1943	17	3	5	5	4
1944	20	4	5	5	6
1945	19	6	5	4	4
1946	21	5	5	5	6
1947	17	4	5	5	3
1948	21	5	4	5	7
1949	19	5	6	4	4
1950	20	5	4	6	5
1951	20	5	5	5	5
1952	16	4	4	4	4
1953	21	5	6	5	5
1954	22	5	5	6	6
1955	19	6	5	3	5
1956	17	4	4	6	3
1957	21	6	5	4	6
1958	18	3	5	5	5
1959	21	7	4	6	4
1960	17	3	6	4	4
1961	19	5	4	4	6
1962	19	5	5	5	4
1963	20	4	5	6	5
1964	19	4	5	4	6
1965	19	6	4	4	5
1966	20	5	5	6	4
1967	19	4	5	4	6
1968	17	5	5	4	3
1969	20	6	3	5	6
1970	18	3	6	4	5
1971	18	4	3	6	5
1972	22	6	6	6	4
1973	19	5	4	5	5
1974	18	4	5	4	5
1975	20	6	5	5	4
1976	20	5	6	4	5
1977	19	4	5	5	5
1978	19	6	5	4	4
1979	18	3	5	5	5
1980	20	6	5	5	4
1981	20	5	4	5	6
1982	19	5	4	5	5
1983	19	5	5	5	4
1984	19	5	5	4	5
1985	19	5	5	4	5
1986	19	4	5	6	4
1987	20	4	6	5	5
1988	18	5	5	3	5
1989	19	5	5	6	3
1990	20	5	4	5	6
1991	17	3	6	3	5
1992	20	6	3	5	6
1993	21	5	6	5	5
1994	18	4	3	6	5
1995	17	5	5	4	3
1996	22	6	5	6	5
1997	19	5	5	3	6
1998	18	5	4	6	3
1999	20	5	5	5	5
2000	20	4	5	5	6
2001	19	5	5	5	4
2002	19	5	4	6	4
2003	19	5	6	3	5
2004	19	6	4	4	5
2005	21	5	5	6	5
2006	18	3	5	5	5
2007	18	5	4	4	5
2008	20	6	5	5	4
2009	19	3	5	5	6
2010	19	4	6	5	4
2011	20	6	4	5	5
2012	18	5	5	4	4
2013	19	4	4	5	6
2014	20	4	6	5	5
2015	20	5	4	6	5
2016	18	5	5	4	4
2017	20	4	5	6	5
2018	18	5	5	3	5
2019	21	5	5	7	4
2020	20	6	5	3	6
2021	17	4	4	5	4
2022	20	6	4	5	5
2023	19	4	6	4	5
2024	19	5	5	4	5
2025	18	5	3	6	4
2026	21	5	6	5	5
2027	19	5	5	4	5
2028	18	5	3	5	5
2029	19	5	5	6	3
2030	18	4	5	3	6
2031	19	6	6	4	3
2032	21	4	5	6	6
2033	20	5	6	5	4
2034	16	4	3	4	5
2035	22	6	5	6	5
2036	19	3	5	5	6
2037	18	5	4	4	5
2038	21	5	5	6	5
2039	18	5	5	3	5
2040	19	4	4	6	5
2041	20	6	5	5	4
2042	19	4	6	5	4
2043	20	6	4	5	5
2044	19	4	5	5	5
2045	19	5	4	5	5
2046	19	5	5	4	5
2047	20	5	5	4	6
2048	19	5	4	5	5
2049	19	4	5	5	5
2050	20	6	5	5	4
2051	18	5	4	3	6
2052	18	4	5	6	3
2053	20	4	5	5	6
2054	18	5	6	4	3
2055	19	6	3	5	5
2056	21	4	6	6	5
2057	18	4	4	5	5
2058	20	6	5	5	4
2059	21	5	6	5	5
2060	18	4	5	4	5
2061	18	4	4	5	5
2062	21	6	6	5	4
2063	18	3	4	5	6
2064	20	6	4	6	4
2065	19	4	5	5	5
2066	20	6	6	3	5
2067	16	4	3	5	4
2068	22	6	5	6	5
2069	18	4	6	3	5
2070	20	5	5	4	6
2071	19	5	4	6	4
2072	19	4	5	5	5
2073	18	5	5	4	4
2074	20	6	4	4	6
2075	20	4	7	5	4
2076	18	5	3	5	5
2077	20	5	6	4	5
2078	19	5	4	5	5
2079	20	4	6	5	5
2080	19	4	4	6	5
2081	19	6	5	4	4
2082	18	4	4	6	4
2083	21	6	5	4	6
2084	18	4	4	5	5
2085	19	6	5	5	3
2086	21	4	6	5	6
2087	19	5	4	5	5
2088	17	5	4	5	3
2089	22	6	6	5	5
2090	17	4	4	4	5
2091	20	5	3	6	6
2092	19	4	6	4	5
2093	21	4	6	5	6
2094	17	6	4	4	3
2095	20	4	5	6	5
2096	18	4	6	3	5
2097	19	6	4	5	4
2098	20	5	5	5	5
2099	18	4	4	5	5
2100	17	4	5	4	4
2101	23	6	6	6	5
2102	20	5	5	4	6
2103	18	4	4	6	4
2104	20	6	5	4	5
2105	18	3	6	5	4
2106	18	5	3	5	5
2107	19	5	4	5	5
2108	19	4	6	5	4
2109	19	5	5	4	5
2110	20	5	4	6	5
2111	18	5	4	5	4
2112	20	6	5	4	5
2113	19	5	5	4	5
2114	20	4	5	5	6
2115	19	5	5	6	3
2116	19	4	5	4	6
2117	19	5	6	4	4
2118	19	4	4	6	5
2119	22	5	6	5	6
2120	18	5	4	4	5
2121	18	6	4	4	4
2122	22	4	6	6	6
2123	16	4	5	3	4
2124	20	5	5	6	4
2125	20	6	5	4	5
2126	19	3	4	6	6
2127	17	6	4	4	3
2128	21	4	6	6	5
2129	19	5	4	4	6
2130	20	6	4	5	5
2131	18	4	5	5	4
2132	20	5	6	4	5
2133	18	5	3	5	5
2134	19	5	4	6	4
2135	21	4	6	4	7
2136	18	5	5	5	3
2137	20	6	3	5	6
2138	18	3	6	5	4
2139	19	5	4	4	6
2140	20	6	6	4	4
2141	20	4	5	6	5
2142	18	5	5	4	4
2143	21	5	5	6	5
2144	19	6	5	4	4
2145	18	3	4	6	5
2146	21	6	5	4	6
2147	18	3	6	5	4
2148	20	6	5	5	4
2149	19	3	4	6	6
2150	19	6	5	4	4
2151	17	4	5	5	3
2152	20	5	5	4	6
2153	19	4	5	4	6
2154	19	6	3	6	4
2155	20	5	6	4	5
2156	18	4	4	4	6
2157	21	6	5	6	4
2158	19	5	4	5	5
2159	18	4	6	4	4
2160	18	6	3	4	5
2161	23	4	7	6	6
2162	17	3	4	5	5
2163	20	6	6	4	4
2164	20	5	4	6	5
2165	19	5	5	3	6
2166	17	5	4	5	3
2167	21	7	5	5	4
2168	19	3	6	4	6
2169	19	6	3	5	5
2170	19	4	6	5	4
2171	20	5	6	5	4
2172	19	5	3	6	5
2173	19	5	4	5	5
2174	18	3	6	4	5
2175	20	5	5	5	5
2176	19	6	4	4	5
2177	20	4	5	5	6
2178	18	4	6	4	4
2179	20	5	4	5	6
2180	19	5	5	5	4
2181	18	5	3	6	4
2182	20	4	6	4	6
2183	18	5	4	4	5
2184	20	5	5	5	5
2185	21	5	5	6	5
2186	18	5	6	3	4
2187	19	5	4	6	4
2188	20	5	5	4	6
2189	18	4	5	5	4
2190	20	6	4	6	4
2191	18	4	5	4	5
2192	20	4	5	5	6
2193	18	6	4	5	3
2194	20	5	6	5	4
2195	19	4	5	4	6
2196	20	5	5	5	5
2197	18	5	4	6	3
2198	20	5	6	3	6
2199	18	5	4	5	4
2200	21	5	4	6	6
2201	18	3	6	4	5
2202	18	5	3	5	5
2203	22	6	6	5	5
2204	20	4	5	6	5
2205	16	4	5	3	4
2206	22	6	5	6	5
2207	19	5	5	3	6
2208	18	3	4	6	5
2209	19	6	6	3	4
2210	20	4	5	6	5
2211	19	6	4	4	5
2212	19	5	4	5	5
2213	19	5	5	4	5
2214	19	5	5	6	3
2215	20	5	4	5	6
2216	17	4	5	4	4
2217	20	4	5	6	5
2218	20	5	6	5	4
2219	19	5	4	4	6
2220	18	5	4	6	3
2221	21	5	5	4	7
2222	17	4	6	3	4
2223	20	5	3	6	6
2224	20	5	6	5	4
2225	17	3	4	5	5
2226	20	6	5	5	4
2227	22	5	5	7	5
2228	18	5	4	3	6
2229	18	4	5	6	3
2230	20	6	4	4	6
2231	20	3	6	5	6
2232	19	6	5	5	3
2233	18	4	5	5	4
2234	19	5	5	3	6
2235	19	5	4	5	5
2236	19	5	4	6	4
2237	19	4	6	4	5
2238	18	5	3	4	6
2239	21	6	6	5	4
2240	19	4	5	5	5
2241	19	5	6	5	3
2242	19	6	3	4	6
2243	18	4	5	5	4
2244	18	4	4	5	5
2245	21	5	6	5	5
2246	20	5	4	5	6
2247	18	4	5	5	4
2248	20	5	5	5	5
2249	20	6	5	4	5
2250	20	5	5	6	4
2251	19	5	5	4	5
2252	17	3	5	4	5
2253	21	7	4	6	4
2254	20	4	5	5	6
2255	19	5	5	4	5
2256	19	5	4	5	5
2257	20	5	6	5	4
2258	20	5	4	5	6
2259	18	5	4	5	4
2260	19	4	6	5	4
2261	18	4	5	3	6
2262	18	5	5	5	3
2263	21	5	4	6	6
2264	20	4	7	4	5
2265	17	5	3	4	5
2266	22	6	5	6	5
2267	18	4	4	5	5
2268	16	4	5	3	4
2269	22	6	4	6	6
2270	19	4	6	4	5
2271	17	4	3	6	4
2272	20	6	5	5	4
2273	19	4	5	5	5
2274	20	5	5	5	5
2275	19	5	5	5	4
2276	20	6	5	4	5
2277	19	5	5	4	5
2278	21	4	6	5	6
2279	17	4	4	5	4
2280	19	5	5	5	4
2281	20	6	4	5	5
2282	18	4	4	4	6
2283	19	5	6	5	3
2284	21	5	5	5	6
2285	17	5	5	3	4
2286	20	5	4	6	5
2287	21	4	7	5	5
2288	17	4	4	5	4
2289	20	6	5	4	5
2290	19	4	5	6	4
2291	18	4	5	3	6
2292	20	5	4	6	5
2293	20	6	5	4	5
2294	17	3	4	5	5
2295	20	6	5	5	4
2296	19	5	5	5	4
2297	21	6	5	4	6
2298	16	5	3	5	3
2299	22	5	5	6	6
2300	19	4	6	4	5
2301	19	4	4	5	6
2302	19	6	4	6	3
2303	19	4	6	4	5
2304	19	6	5	4	4
2305	20	5	4	5	6
2306	19	4	6	5	4
2307	17	4	4	4	5
2308	21	6	5	5	5
2309	20	4	5	6	5
2310	20	5	5	5	5
2311	19	4	5	5	5
2312	18	6	4	3	5
2313	19	3	5	7	4
2314	19	5	5	4	5
2315	19	4	5	5	5
2316	19	6	4	5	4
2317	20	3	6	5	6
2318	19	5	5	5	4
2319	19	6	4	5	4
2320	21	6	5	4	6
2321	17	4	4	4	5
2322	19	5	4	5	5
2323	20	5	6	5	4
2324	20	4	5	4	7
2325	17	5	4	5	3
2326	21	5	5	6	5
2327	19	5	6	4	4
2328	18	6	3	4	5
2329	19	4	5	6	4
2330	20	5	5	4	6
2331	17	5	5	4	3
2332	23	6	6	6	5
2333	18	4	5	4	5
2334	17	3	4	5	5
2335	22	7	5	5	5
2336	19	3	5	6	5
2337	18	5	3	5	5
2338	19	4	5	4	6
2339	19	5	6	4	4
2340	19	5	4	5	5
2341	21	6	5	6	4
2342	17	4	5	4	4
2343	22	6	5	5	6
2344	18	4	4	5	5
2345	19	5	4	5	5
2346	19	4	6	5	4
2347	20	5	4	4	7
2348	19	5	6	4	4
2349	19	5	3	6	5
2350	21	5	7	4	5
2351	17	5	3	4	5
2352	19	5	5	5	4
2353	20	4	5	6	5
2354	17	5	5	3	4
2355	20	5	4	6	5
2356	21	5	6	5	5
2357	18	3	4	6	5
2358	19	7	4	5	3
2359	20	4	6	5	5
2360	19	4	5	4	6
2361	18	5	5	4	4
2362	20	5	5	6	4
2363	20	5	5	4	6
2364	18	4	3	6	5
2365	19	5	5	5	4
2366	21	5	6	4	6
2367	17	5	4	4	4
2368	20	5	4	6	5
2369	20	4	7	4	5
2370	19	5	4	5	5
2371	20	6	5	4	5
2372	17	3	4	6	4
2373	19	5	6	3	5
2374	21	6	5	5	5
2375	20	6	5	4	5
2376	18	4	4	6	4
2377	19	5	5	3	6
2378	20	4	6	5	5
2379	19	5	4	6	4
2380	19	4	4	6	5
2381	18	5	5	4	4
2382	19	5	5	5	4
2383	21	5	5	5	6
2384	18	5	4	4	5
2385	19	6	4	5	4
2386	21	5	6	5	5
2387	19	3	5	5	6
2388	19	6	4	6	3
2389	19	5	5	4	5
2390	19	4	5	5	5
2391	18	5	3	5	5
2392	22	4	6	6	6
2393	18	4	5	4	5
2394	18	6	5	3	4
2395	21	4	5	7	5
2396	19	5	6	3	5
2397	17	5	4	5	3
2398	20	7	4	4	5
2399	18	2	5	5	6
2400	18	5	4	5	4
2401	22	5	6	6	5
2402	19	5	5	4	5
2403	20	5	4	6	5
2404	18	5	5	4	4
2405	19	4	6	5	4
2406	19	5	4	4	6
2407	18	5	4	5	4
2408	20	4	5	5	6
2409	19	5	6	5	3
2410	20	5	3	5	7
2411	17	4	5	5	3
2412	20	6	4	5	5
2413	20	5	6	4	5
2414	19	5	4	5	5
2415	18	4	5	5	4
2416	21	4	6	5	6
2417	19	6	6	3	4
2418	19	4	4	7	4
2419	21	6	5	4	6
2420	17	3	5	4	5
2421	21	7	4	5	5
2422	18	3	5	5	5
2423	20	5	5	5	5
2424	17	5	5	4	3
2425	20	5	5	5	5
2426	20	4	5	5	6
2427	19	6	4	5	4
2428	18	4	5	5	4
2429	21	5	5	4	7
2430	19	5	5	5	4
2431	19	5	3	6	5
2432	18	4	7	3	4
2433	18	5	2	5	6
2434	22	5	6	6	5
2435	19	4	4	6	5
2436	18	5	5	4	4
2437	20	6	4	5	5
2438	19	4	5	4	6
2439	18	4	5	5	4
2440	21	7	6	4	4
2441	19	4	5	5	5
2442	19	5	4	5	5
2443	19	4	5	5	5
2444	20	6	5	5	4
2445	19	5	4	6	4
2446	20	4	5	5	6
2447	18	4	6	3	5
2448	20	5	5	6	4
2449	20	5	5	5	5
2450	18	4	5	4	5
2451	18	5	5	5	3
2452	20	5	5	4	6
2453	18	4	5	4	5
2454	18	5	2	6	5
2455	21	5	7	4	5
2456	19	4	4	5	6
2457	19	6	4	5	4
2458	22	6	5	7	4
2459	16	4	5	2	5
2460	19	5	5	5	4
2461	21	5	5	5	6
2462	19	4	5	5	5
2463	19	5	5	5	4
2464	19	5	4	5	5
2465	20	4	6	4	6
2466	18	6	3	5	4
2467	20	6	5	5	4
2468	19	4	6	4	5
2469	20	5	4	5	6
2470	18	5	5	5	3
2471	19	4	6	4	5
2472	20	5	5	6	4
2473	20	5	4	5	6
2474	18	4	5	5	4
2475	18	5	4	4	5
2476	20	5	5	4	6
2477	20	4	4	6	6
2478	18	4	6	4	4
2479	21	5	5	6	5
2480	18	6	4	3	5
2481	19	4	4	7	4
2482	19	5	6	3	5
2483	19	4	5	5	5
2484	20	7	3	5	5
2485	19	4	5	5	5
2486	19	4	6	4	5
2487	20	6	4	6	4
2488	19	5	5	4	5
2489	19	4	5	5	5
2490	19	5	4	5	5
2491	19	5	6	5	3
2492	19	4	4	4	7
2493	17	5	5	5	2
2494	21	5	5	5	6
2495	20	5	7	4	4
2496	17	4	3	5	5
2497	21	6	5	6	4
2498	18	4	5	4	5
2499	19	5	5	4	5
2500	22	5	4	7	6
2501	19	5	5	4	5
2502	16	3	4	5	4
2503	21	7	5	4	5
2504	20	3	6	6	5
2505	20	6	5	5	4
2506	18	4	5	4	5
2507	20	6	4	4	6
2508	19	4	5	5	5
2509	19	4	5	5	5
2510	19	5	5	4	5
2511	19	5	4	5	5
2512	21	6	5	5	5
2513	17	4	4	4	5
2514	18	5	6	5	2
2515	21	5	4	5	7
2516	17	4	5	4	4
2517	19	5	4	6	4
2518	23	5	7	6	5
2519	16	4	3	4	5
2520	19	5	4	5	5
2521	21	5	6	5	5
2522	19	5	5	4	5
2523	19	5	4	5	5
2524	19	5	5	5	4
2525	17	2	5	4	6
2526	21	7	5	6	3
2527	20	5	4	6	5
2528	20	5	5	4	6
2529	17	4	4	5	4
2530	21	6	5	5	5
2531	19	4	5	4	6
2532	19	4	5	5	5
2533	19	5	5	5	4
2534	19	4	6	4	5
2535	18	5	4	5	4
2536	19	6	3	5	5
2537	18	3	7	4	4
2538	19	5	4	4	6
2539	21	6	5	5	5
2540	19	5	4	6	4
2541	19	5	6	4	4
2542	20	5	4	5	6
2543	19	5	5	4	5
2544	18	4	4	7	3
2545	19	5	5	4	5
2546	19	4	5	4	6
2547	20	5	5	6	4
2548	19	4	5	5	5
2549	20	6	5	4	5
2550	19	6	4	5	4
2551	22	5	6	5	6
2552	15	3	4	4	4
2553	20	6	4	5	5
2554	20	5	5	5	5
2555	21	4	5	5	7
2556	17	5	5	4	3
2557	21	5	5	6	5
2558	19	5	5	4	5
2559	19	5	4	5	5
2560	19	4	6	5	4
2561	20	5	5	5	5
2562	16	5	4	3	4
2563	22	5	5	7	5
2564	19	4	6	3	6
2565	19	4	4	6	5
2566	20	7	4	4	5
2567	18	3	5	6	4
2568	18	5	4	4	5
2569	19	5	5	4	5
2570	20	5	5	5	5
2571	17	4	4	5	4
2572	21	5	5	6	5
2573	18	5	5	4	4
2574	20	5	4	5	6
2575	19	5	5	5	4
2576	19	5	5	4	5
2577	20	5	6	5	4
2578	21	4	5	5	7
2579	17	5	5	4	3
2580	17	4	4	5	4
2581	23	6	6	5	6
2582	18	4	4	5	5
2583	19	6	4	5	4
2584	21	5	6	5	5
2585	16	5	4	2	5
2586	21	4	5	7	5
2587	20	5	6	5	4
2588	18	3	5	5	5
2589	19	7	4	4	4
2590	20	3	6	6	5
2591	17	4	4	4	5
2592	20	6	5	4	5
2593	19	5	4	5	5
2594	20	5	5	4	6
2595	17	4	4	5	4
2596	20	6	5	6	3
2597	20	5	5	3	7
2598	18	5	4	5	4
2599	20	5	4	6	5
2600	20	4	7	5	4
2601	19	5	3	5	6
2602	19	5	5	5	4
2603	19	4	5	5	5
2604	20	6	6	4	4
2605	21	6	5	5	5
2606	18	5	4	4	5
2607	18	3	5	5	5
2608	20	6	5	4	5
2609	20	4	5	6	5
2610	19	5	4	6	4
2611	19	3	5	5	6
2612	18	6	5	3	4
2613	18	4	4	6	4
2614	21	5	6	5	5
2615	18	4	5	4	5
2616	20	6	4	5	5
2617	19	4	5	5	5
2618	19	4	5	5	5
2619	19	5	5	5	4
2620	20	6	4	4	6
2621	20	4	6	5	5
2622	17	6	2	5	4
2623	21	4	7	5	5
2624	18	4	4	4	6
2625	19	5	6	4	4
2626	20	5	4	7	4
2627	20	6	6	3	5
2628	17	5	3	5	4
2629	21	6	5	5	5
2630	18	3	5	5	5
2631	18	6	4	4	4
2632	21	5	6	5	5
2633	19	4	5	5	5
2634	17	4	4	5	4
2635	21	6	5	5	5
2636	19	4	5	5	5
2637	19	4	4	5	6
2638	19	5	5	4	5
2639	20	5	5	5	5
2640	18	5	5	4	4
2641	21	5	4	6	6
2642	18	4	6	4	4
2643	20	6	4	6	4
2644	21	5	5	5	6
2645	16	4	3	5	4
2646	19	4	6	4	5
2647	22	5	6	5	6
2648	19	6	5	3	5
2649	19	5	3	7	4
2650	20	5	6	3	6
2651	17	4	5	4	4
2652	20	6	3	6	5
2653	18	4	5	5	4
2654	19	4	5	5	5
2655	19	6	5	4	4
2656	20	4	5	6	5
2657	18	4	4	5	5
2658	20	6	5	5	4
2659	19	5	5	5	4
2660	21	4	6	4	7
2661	18	5	5	5	3
2662	19	5	4	5	5
2663	19	4	6	4	5
2664	19	4	3	6	6
2665	21	5	5	6	5
2666	19	5	5	5	4
2667	17	5	4	3	5
2668	21	5	5	6	5
2669	20	5	6	4	5
2670	18	4	5	5	4
2671	20	7	5	3	5
2672	18	3	4	6	5
2673	18	5	5	4	4
2674	21	5	5	5	6
2675	20	6	5	4	5
2676	19	5	4	6	4
2677	18	4	5	4	5
2678	20	5	6	4	5
2679	19	5	4	5	5
2680	19	4	5	6	4
2681	19	4	5	4	6
2682	19	6	5	6	2
2683	20	5	4	4	7
2684	17	4	5	4	4
2685	20	6	3	5	6
2686	21	5	7	5	4
2687	20	4	4	6	6
2688	17	5	4	5	3
2689	22	5	6	6	5
2690	18	5	5	3	5
2691	18	4	4	6	4
2692	21	6	4	5	6
2693	18	3	6	4	5
2694	19	6	5	4	4
2695	19	4	4	6	5
2696	20	5	6	4	5
2697	17	5	4	4	4
2698	20	6	4	5	5
2699	19	3	6	5	5
2700	18	5	3	5	5
2701	20	5	6	5	4
2702	19	4	5	4	6
2703	21	5	6	6	4
2704	19	5	4	5	5
2705	18	5	6	4	3
2706	18	5	3	4	6
2707	21	4	6	5	6
2708	18	4	3	6	5
2709	19	5	6	5	3
2710	20	5	4	5	6
2711	18	5	4	4	5
2712	19	5	5	6	3
2713	21	6	6	4	5
2714	18	4	5	4	5
2715	20	6	3	6	5
2716	18	3	6	4	5
2717	19	5	6	4	4
2718	21	6	4	6	5
2719	19	4	5	5	5
2720	19	4	5	4	6
2721	20	6	4	5	5
2722	19	5	5	5	4
2723	18	3	5	4	6
2724	18	5	6	4	3
2725	20	5	5	5	5
2726	21	5	6	5	5
2727	16	5	2	5	4
2728	21	5	6	5	5
2729	20	4	5	5	6
2730	18	5	4	4	5
2731	22	6	4	7	5
2732	17	4	6	3	4
2733	18	4	4	5	5
2734	20	6	4	5	5
2735	20	4	5	6	5
2736	19	5	5	5	4
2737	18	5	4	4	5
2738	21	5	5	5	6
2739	18	5	4	5	4
2740	20	5	6	4	5
2741	19	5	5	4	5
2742	20	4	5	6	5
2743	18	5	4	5	4
2744	19	5	5	4	5
2745	19	5	5	6	3
2746	21	4	5	5	7
2747	18	4	6	4	4
2748	19	6	4	5	4
2749	22	5	6	5	6
2750	17	3	4	5	5
2751	18	5	5	4	4
2752	21	5	6	6	4
2753	18	5	4	3	6
2754	18	4	3	6	5
2755	20	6	6	4	4
2756	19	3	5	5	6
2757	20	7	4	5	4
2758	19	5	4	6	4
2759	20	5	6	3	6
2760	17	5	4	5	3
2761	22	6	5	5	6
2762	17	3	5	4	5
2763	20	4	5	5	6
2764	20	6	5	5	4
2765	20	4	5	5	6
2766	17	5	4	5	3
2767	20	6	4	4	6
2768	18	4	7	4	3
2769	20	5	4	5	6
2770	20	6	5	5	4
2771	18	4	5	5	4
2772	21	5	6	5	5
2773	20	4	4	6	6
2774	19	6	4	4	5
2775	17	3	5	6	3
2776	19	6	4	3	6
2777	19	3	5	5	6
2778	21	6	5	6	4
2779	18	3	6	4	5
2780	19	6	4	4	5
2781	19	5	4	6	4
2782	20	5	5	5	5
2783	17	4	5	3	5
2784	20	6	3	5	6
2785	21	5	6	5	5
2786	19	3	5	5	6
2787	18	6	5	5	2
2788	20	5	4	5	6
2789	19	4	6	4	5
2790	18	5	4	5	4
2791	21	5	6	6	4
2792	19	5	4	4	6
2793	16	4	4	4	4
2794	22	6	6	6	4
2795	20	5	6	4	5
2796	18	4	4	5	5
2797	19	6	4	5	4
2798	19	3	6	5	5
2799	19	6	4	5	4
2800	20	5	4	5	6
2801	19	4	5	5	5
2802	18	4	5	4	5
2803	20	6	5	5	4
2804	20	5	5	5	5
2805	20	5	5	5	5
2806	18	4	5	4	5
2807	20	5	5	4	6
2808	19	4	5	6	4
2809	20	5	4	5	6
2810	17	4	6	3	4
2811	19	5	4	5	5
2812	23	6	6	5	6
2813	17	5	3	5	4
2814	17	5	5	4	3
2815	22	5	5	6	6
2816	17	4	5	3	5
2817	20	5	4	7	4
2818	20	5	6	5	4
2819	18	3	4	5	6
2820	19	6	4	5	4
2821	20	4	5	6	5
2822	18	5	5	3	5
2823	20	6	5	4	5
2824	20	4	5	6	5
2825	18	4	5	4	5
2826	18	5	4	5	4
2827	20	6	4	6	4
2828	20	4	5	4	7
2829	18	4	5	5	4
2830	21	6	4	6	5
2831	19	4	6	4	5
2832	19	4	4	5	6
2833	19	5	6	4	4
2834	19	4	5	6	4
2835	19	6	5	3	5
2836	19	5	4	6	4
2837	18	5	5	3	5
2838	20	4	5	6	5
2839	19	6	4	3	6
2840	19	4	5	6	4
2841	20	6	5	5	4
2842	19	4	5	5	5
2843	19	6	4	4	5
2844	17	4	4	6	3
2845	21	4	6	5	6
2846	18	5	5	3	5
2847	20	5	4	6	5
2848	19	5	5	5	4
2849	19	4	5	4	6
2850	20	6	5	5	4
2851	21	5	5	5	6
2852	18	4	5	5	4
2853	16	5	3	4	4
2854	23	5	6	6	6
2855	20	4	5	5	6
2856	19	6	5	4	4
2857	19	4	5	6	4
2858	20	6	5	3	6
2859	18	4	4	6	4
2860	20	6	5	5	4
2861	18	3	6	4	5
2862	18	6	3	4	5
2863	21	4	6	6	5
2864	19	4	5	5	5
2865	19	5	4	5	5
2866	19	6	4	4	5
2867	19	4	5	5	5
2868	18	4	5	4	5
2869	20	6	5	5	4
2870	19	5	4	4	6
2871	18	4	5	5	4
2872	20	4	4	6	6
2873	19	5	6	5	3
2874	19	6	3	5	5
2875	20	4	6	5	5
2876	18	5	4	4	5
2877	20	5	6	5	4
2878	22	5	6	5	6
2879	17	5	5	3	4
2880	18	4	4	6	4
2881	21	6	6	4	5
2882	18	4	4	5	5
2883	20	6	3	6	5
2884	19	4	6	4	5
2885	19	5	5	4	5
2886	18	5	4	5	4
2887	21	5	6	6	4
2888	17	3	5	4	5
2889	20	6	5	4	5
2890	19	4	5	6	4
2891	20	5	5	4	6
2892	17	4	5	4	4
2893	20	6	3	5	6
2894	20	4	7	4	5
2895	18	5	2	6	5
2896	20	5	6	5	4
2897	19	5	4	5	5
2898	19	5	5	4	5
2899	19	5	4	6	4
2900	20	5	6	4	5
2901	19	4	4	6	5
2902	21	6	6	4	5
2903	18	4	4	6	4
2904	19	6	5	4	4
2905	20	5	5	4	6
2906	19	5	4	5	5
2907	18	4	5	5	4
2908	20	5	5	5	5
2909	19	5	5	4	5
2910	19	4	4	6	5
2911	20	4	6	5	5
2912	19	5	5	4	5
2913	18	6	4	5	3
2914	20	4	5	5	6
2915	18	3	6	4	5
2916	20	6	3	6	5
2917	20	5	6	4	5
2918	18	3	4	6	5
2919	18	5	5	4	4
2920	23	6	6	6	5
2921	18	5	4	3	6
2922	18	5	4	6	3
2923	20	5	5	4	6
2924	19	4	6	4	5
2925	18	5	4	5	4
2926	19	5	4	6	4
2927	20	5	6	4	5
2928	19	6	4	4	5
2929	20	5	4	6	5
2930	18	4	5	5	4
2931	18	5	4	4	5
2932	20	6	6	4	4
2933	20	3	6	5	6
2934	19	5	5	6	3
2935	19	5	4	4	6
2936	19	5	5	5	4
2937	19	4	4	5	6
2938	20	4	5	5	6
2939	19	5	4	5	5
2940	18	5	5	4	4
2941	22	5	5	6	6
2942	18	5	5	4	4
2943	19	5	5	6	3
2944	21	6	5	4	6
2945	17	3	4	5	5
2946	19	6	4	5	4
2947	21	4	6	5	6
2948	18	5	5	3	5
2949	20	6	3	6	5
2950	19	4	6	4	5
2951	20	5	5	5	5
2952	18	6	3	4	5
2953	18	4	5	6	3
2954	19	3	5	4	7
2955	19	6	6	5	2
2956	20	5	4	5	6
2957	19	4	6	5	4
2958	18	5	3	5	5
2959	21	6	6	5	4
2960	20	4	5	5	6
2961	17	4	5	4	4
2962	22	5	5	6	6
2963	19	5	6	4	4
2964	17	3	3	6	5
2965	21	7	4	5	5
2966	18	3	6	5	4
2967	20	6	5	4	5
2968	18	4	4	5	5
2969	21	6	5	5	5
2970	18	5	5	4	4
2971	20	5	5	4	6
2972	19	4	5	5	5
2973	19	5	4	6	4
2974	19	5	5	4	5
2975	19	5	5	3	6
2976	20	5	6	6	3
2977	19	4	4	5	6
2978	18	5	6	3	4
2979	19	6	3	5	5
2980	23	4	7	6	6
2981	15	3	3	5	4
2982	20	6	5	5	4
2983	20	5	5	5	5
2984	19	5	4	4	6
2985	18	5	4	5	4
2986	21	6	6	5	4
2987	19	3	5	5	6
2988	20	6	4	6	4
2989	18	4	5	5	4
2990	21	6	6	4	5
2991	17	5	3	5	4
2992	21	4	4	6	6
2993	18	3	6	3	6
2994	20	5	5	5	5
2995	19	6	4	5	4
2996	19	3	6	5	5
2997	18	5	5	4	4
2998	19	6	3	4	5
2999	19	4	6	5	4
3000	17	4	3	5	5
3001	21	5	6	5	5
3002	20	5	5	5	5

The large table shown above, with high values shaded in shades of grey and low values shaded in shades of red, is impossible to describe in detail in words. Nevertheless, some points can be made:

1. the number of potential primes in some centuries is fewer than those of (other) actual centuries between 200 and the “eight-digit gap”:
1. four moduli 3003 have only fifteen potential primes, and forty-six have only sixteen potential primes after numbers divisible by primes up to 13 are removed
2. it is clear than no century can have more then 23 primes based upon divisibility by primes up to 13
1. nonetheless, there are 26 moduli 3003 that could theoretically have 23 primes, yet it is known only 20 possible patterns exist for a 23-prime century per OEIS A261571
3. there are 48 possible moduli 3003 for seven primes ending in each of 1, 3, 7, or 9
4. contrariwise, for primes ending in each of 1, 3, 7, or 9, there are twelve moduli 3003 which yield merely two possible primes ending in each digit, and 188 moduli 3003 which yield merely three possible primes
5. there seems to be a pattern relating n mod (3003) and (3003-n) mod (3003), although this would be very hard to check
6. small centuries often do conform with exceptions based on number of potential primes:
1. for instance, the 22nd century is the first with only ten primes, and has only fifteen potential primes
2. the 187^th, 189^th, 315^th, 696^th and 1560^th centuries all have a record fewest primes for such a small century, and have only seventeen potential primes
3. the 798^th century, the third with only three primes, has only sixteen potential primes
4. however, the 1573^rd century has fifteen primes — the equal most between 23,100 and 783,699 — yet also has only seventeen potential primes
5. the 80563^rd century with seven primes ending in 1 and none ending in 3, has only three potential primes ending in 3 [80562 is congruent to 2484 mod (3003)]

I have not yet checked moduli (3003) for centuries above the “eight-digit gap”, and doing so would be highly arduous because the number of possible moduli is very large. Doing the less cumbersome moduli (21) and (231) did give expected results, and I would not expect a different result with the more accurate moduli (3003).