Tuesday, 26 December 2023

Why no anarcho-capitalism before the 1970s?

In Commerce and Coalitions, Ron Rogowski argued on pages 165 to 168 that socialism never evolved in the United States because of the enduring abundance of land and scarcity of labour. Whilst Rogowski is too timid about discussing race — for a start, the theories of Eli Heckscher and Bertil Ohlin, and later Wolfgang Stolper and Paul Samuelson, are in no way inconsistent with division on the basis of race if ownership of production factors be divided thereby — he does offer quite reasonable explanations in terms of how labour loses from trade and becomes either timid or powerless except during falling trade.

One related point I thought of on reading Rogowski but which has not been discussed is why anarcho-capitalism evolved where and when it did. Since the Republican Revolution, anarcho-capitalism has been a highly influential ideology amongst the US ruling class, with Randolph Hohle arguing that anarcho-capitalist and allied writers use a code of:

“private” = “White”

“public” = “Black”
to justify their vision of a society without public services. (Although Hohle says this code developed only after the civil rights revolution of the middle 1960s, I feel that it probably dates back to at least the early Republic when free blacks, as I noted previously, became viewed as wholly deviant.)

Despite its influence, anarcho-capitalism has never been subject to detailed scholarly study. The critical question is why, given the benefits not having to pay taxes would have to the extremely rich, anarcho-capitalism only became an established ideology in the 1970s, and never evolved in Europe or Japan at all. Here, Rogowski can provide a very clear answer. Anarcho-capitalism is, by definition, a militant movement of the upper classes to remove the power of labour, and in its goal to eliminate the public sector is the direct opposite of socialist movements aiming to eliminate the private sector. By inverting what Commerce and Coalitions says about socialism, we can predict logically that anarcho-capitalism (or similar militant movements against democracy) will arise where(ever) capital benefits from expanding trade and labour does not, that is, where capital is abundant and labour scarce. In Rogowski’s terminology, anarcho-capitalism will arise in advanced economies with a high land:labour ratio. Under these conditions, capital and land gain from free trade, whilst labour sees its opportunities restricted and its incomes reduced. Thus class struggle is intense as capital and land seek to eliminate the power of groups opposed to their unlimited power by funding politicians so dedicated, and ultimately to destroy all possible sources of power of such groups. Under this condition, those who do not lie at the very bottom of society — lacking the resources to unite with those who do as their skills are devalued — will stigmatise those at the very bottom. Rogowski himself showed that this stigmatisation can be extremely powerful on page 85 of his 1974 Rational Legitimacy: A Theory of Political Support, and on page 157 he suggests that the probability of a coalition between lower classes with different stigmatisation states is likely to be very low if the groups lack combined economic power.

As I have discussed here, there were never any advanced economies with even a relatively high land:labour ratio at any point between the birth of Christ and about 1900. An undated file from the University of Michigan noted this at PS 489.1 (page 5):
“Abundance of Land and Capital, Scarcity of Labor (p. 32):

Who?
  1. 1840: no one
  2. 1914: US and Canada
  3. [1991-: US and Canada, Australia and New Zealand, Arab Gulf States, Russia, Kazakhstan, Turkmenistan, Turkey (marginal)]”
Thus, before 1900 no state favourable to the development of strong and/or influential anarcho-capitalist type movements existed. Although Proudhon’s ideas as depicted by Marxist Left Review strikingly resemble anarcho-capitalism in many respects, if Rogowski be correct then Proudhon was planting an ideological seed onto the unfavourable soil of mid-nineteenth-century France.

In the developed countries of northwestern Europe, enduring abundance of labour meant that when trade expanded, enriched workers pressed for and gained more rights and a larger public sector. Additionally, labour did not oppose capital because both benefitted from trade, and this made capital compromise severely with labour’s opposing demands for the highest possible taxes and greatest regulation. This is even more emphatically true of later-developing East Asia.

In a labour-rich society, labour opposes capital only when capital is scarce. There capital becomes militant only during falling trade and is intensely protectionist. This militant capital will then support autarky with only the most restricted possible trade, a position entirely opposed to free-trading anarcho-capitalism. Unlike anarcho-capitalism, Marxian socialism was and is not explicitly pro-free trade. Thus one could theoretically imagine militant socialism arising in advanced, land-rich economies under falling trade, though history does not provide an example and there exist many reasons why this would not happen even if the falling trade were extremely prolonged. Thus, “no anarcho-capitalism in labour-rich societies” is almost certainly a more rigid rule than “no militant socialism in labour-scarce societies”.

The rule that there is no anarcho-capitalism in labour-abundant societies can also be extended to other forms of ruling class militancy like religious fundamentalism. This also first emerged in the United States after it became abundant in capital, notably with the second Ku Klux Klan, and re-emerged there after the postwar globalisation. It has been the dominant force in the Gulf monarchies since the pivotal oil crises of the 1970s. These movements argue, at least implicitly, that God’s law decrees a natural hierarchy based on non-class distinctions like race, gender or religion, and that this is a natural order for all human societies.

Sunday, 10 December 2023

The problem of “don’t ask” just from fearing no

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.

The tantrum, with familiar phrases (mantras) like:

“get the word “can” out of your head”

“there’s no such word as “can””

and less familiar mantras like

“I used to be able to [remember to come down] but I can’t now”

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.

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 hope I becoming less bad at it.

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.

When I look at it logically, I recognise how I was obsessed with watching football and possessed zero desire 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 surprised that the rissoles had nearly burned over!

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, anything 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.

However, the most notable lesson from tonight’s tempera tantrum was that my consistent refusal to ask my mother whether she would either:
  1. remind me by coming up to the study or
  2. look after my cooking
out of fear of being told “no” is really, really bad. It might be wise 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 partially justifiable fear of being told “no” — to ask my mother to watch over my cooking. Instead, I assume she will do so as my slave. 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??

Friday, 27 October 2023

The “Australia shock”

Following on from his Commerce and Coalitions, of which I wrote several discussions earlier in 2023, I have recently been looking at the preview of Ron Rogowski’s new book Shocking Contrasts: Political Responses to Exogenous Supply Shocks.

In many ways Shocking Contrasts is intended as an expansion of what Rogowski discussed over three decades earlier in Commerce and Coalitions. His earlier book looked at how endowment affect politics in differently-endowed societies, whilst Shocking Contrasts deals with changes in national and global endowments of important production factors. The book covers chiefly the Black Death in late medieval Europe and the blockade and quest for Lebensraum in interwar Germany, but also looks at the post-Máo Zédōng “China shock”, the fifteenth-century invention of the printing press, and the “railway revolution” of nineteenth-century Russia.

Some years ago, my mother liked to say that “the world is made in China”, upon seeing

“Made in China — Fabrique en Chine [French]”

on virtually every product we bought from stores like Myer and David Jones.

If China has a unique abundance of labour, Australia has an even more unique abundance of land. On page 162 of Handbook on East Asian Economic Integration (edited by Kimura Fukunari, Mari Pangestu, Shandre M. Thangavelu and Christopher Findlay), it is noted that World Bank statistics reveal Australia to possess:

  1. twenty-nine times the global average of agricultural land per capita
  2. sixteen times the global average of mineral resource endowments per capita
  3. eighteen times the global average of land per worker

Page 94 of Commerce and Coalitions revealed Australia as having the second-lowest population per unit area of agricultural land, behind only Botswana.

Thus, the opening up of Australia’s land — preindustrially useless because of extreme deficiency of essential nutrients in its ancient soils and absence of the advanced technology required to smelt the lithophile metals (aluminum, manganese, titanium) in which Australia is so rich — would be expected to constitute a shock of increased land supply. This process began in the 1850s as new land was opened for grazing and continued intensely until at least 1975. In many ways, especially in Queensland where new land is still being cleared for farming, this “Australia shock” (as I will call it) continues to the present.

Shocking Contrasts illustrates no example of a supply shock involving gain of land. The “Australia shock” is probably too prolonged to be sufficiently unexpected for inclusion. Gain of land via trade between 1850 and World War I has been noted by Jeffrey Gale Williamson and subsequently Kevin Hjortshøj O‘Rourke as radically reducing rents in land-poor trade-open European nations. However, both those authors focused on the “New World” as a whole, although this “New World” is comprises two radically different groups of lands:

  1. the New World proper, or the Western Hemisphere of the Americas and New Zealand, which are fertile regions sparsely populated because:
    1. they were peopled very late as either ice sheets or deep seas had to be crossed, and
    2. outside the altiplano native large animals were invariably too egalitarian in social structure for domestication
  2. Australia and Africa, more accurately named the “Ancient World”: early-peopled lands whose low fertility and ecological fragility inhibited technological or human cultural development

All the scholars noted previously demonstrate dramatic increases in inequality in the Ancient and New Worlds, and comparably dramatic decreases in the Old World. The situation before World War I is then contrasted with the interwar situation whereby the Ancient and New Worlds experienced egalitarian trends, and the Old World inegalitarian. Nevertheless, even admitting the importance of interwar deglobalisation, technological developments were continuously increasing Australia’s relative abundance of land: for instance, titanium metal could not be smelted commercially until the 1940s, and large areas of southern Australia could not be farmed until chalcophile micronutrient deficiencies were discovered in the 1950s. By then little potential farmland in the temperate New World remained uncleared as remaining land was invariably too wet, cold or steep for any sort of farming, while the hemisphere’s chalcophile ores were rapidly depleting. These trends have accelerated since the middle 1970s.

Evidence:

If there has been an “Australia shock”, we should see evidence that returns to land have demonstrably fallen. Rogowski shows re the “China shock” that wages have fallen and inequality risen even in other labour-abundant nations, suggesting that their labour is out-competed by China.

Falling Returns to Land:

Evidence of falling returns to land ever since the opening of Australia is very well documented for land-scarce Europe and East Asia. However, the trend can also be seen in the economic history of the New World proper, where areas least able to diversify beyond specialisation in agriculture have seen the sharpest declines in global economic rank, as noted by John Singleton for New Zealand, and much more widely for Argentina. Excluding probably Kazakhstan, no nation rivals New Zealand and the Southern Cone for high agricultural land value per capita (see page 162 of Handbook on East Asian Economic Integration and NationMaster’s comparison here for justification).

As Jeffrey G. Williamson noted in the 1990s, increases in total land value in the most land-rich regions under globalisation can reach orders of magnitude. Strong evidence of falling returns to land can be seen in the political strengthening of landless peasants in land-rich parts of Latin America under postwar rising trade, most notably in Nicaragua during the 1970s and Bolivia during the 1990s. This contrasts sharply with the weakness of labour in these regions during the pre-World War I globalisation, and on page 115 of Commerce and Coalitions Rogowski says:

“Nicaragua, as a thinly populated state, should have experienced a radicalization of land rather than labo[u]r”

Despite the growth of trade after World War II, landowners in Latin America were faced with decreasing returns due to to increased global abundance of land and their inability to own newly usable land and ores. Peasants in land-rich nations, who used but did not own land, would benefit from this trend and increasing returns to the labour they owned. Similar trends can be detected in other land-rich Latin American nations, most of which democratised late in the twentieth century, and also in Afghanistan, where the war between the PDPA and the mujahiddin can be understood as an economic conflict between:

  • diminishing returns to land (via the “Australia shock”) and
  • economic gains of abundant land against scarce capital and labour (via expanding trade)
Certain other land-rich nations — notably Algeria and 1970s Ethiopia — experienced similar effects as  users of land over owners became favoured by increasing global abundance of land at a time when climatic conditions in Australia were unusually favourable.

Impoverishment of Backward, Land-Abundant Societies:

More consistent than unpredicted radicalisation of landless peasants in some land-rich societies has been the plain impoverishment of sub-Saharan Africa and Latin America since World War II. Previously, their per capita incomes and living standards were generally higher than labour-rich tropical Asia and even mainland East Asia. However, with the increasing supply of farmland and lithophile minerals from Australia, those regions became faced with a loss–loss scenario. Their comparative advantages in agriculture and non-lithophile minerals declined, whilst their comparative disadvantages in labour-, capital- or skill-intensive industries did not. The result, as has been noted by many economists, is an impoverishment that (as noted above) extended to what before the Second World War were some of the wealthiest nations in the world.

Rogowski in Commerce and Coalitions attributes some of this impoverishment to protectionist policies favouring the urban elite, but gives little idea as to why the free-trading rural sectors failed to gain political control, and zero idea of why they were challenged after they did in many Latin American nations (e.g. by Shining Path in Peru). Sharica Sudan under Omar Bashir and Iran under the ayatollahs, although imperfect cases due to US sanctions (which I previously argued to have only a minor effect), do not suggest “traditionalist” regimes would have fared better than those based upon the capital–labour coalition. If we assume a continuous gain of land from Australia, we do see that countries less land-surfeited than Australia, but unable to specialise elsewhere, will ipso facto be outcompeted and become poorer. Policies designed to increase competitiveness are likely to be difficult to implement. For instance, radical currency devaluations to make exports more competitive with more land-abundant rivals will be painful even for the very richest, and have never been observed even with IMF structural adjustment, as noted by the IMF’s own Independent Evaluation Office in 2007. Similarly, there are limits to which already low farming and mining wages can fall, and to how much these will restore preceding profitability.

Global Warming:

A third aspect of the “Australia Shock”, more obvious than the previous two, is global warming. Australia, is, of course — excluding the Gulf States — the worst offender in greenhouse gas emissions, with per-citizen emissions ten times the global average. However, Australia’s role in global warming is even greater than this because:
  1. it has been documented that Australian flora is the most efficient in the world at storing carbon
  2. increasingly intense forest fires as observed in 2019 and last September are likely to severely effect carbon storage be removing even small areas of fire-sensitive rainforests
  3. Australia has the largest total area of agricultural land in the world and thus the largest area of native vegetation cleared for farming or grazing
  4. the superabundance of land in Australia has led to protein production increasingly using Australian land instead of Asian or European labour
  5. the extreme abundance of lithophile metals whose smelting is extremely energy-intensive has caused them to substantially supplant scarce easily smelted chalcophile metals, and likely eliminated incentives for recycling chalcophiles

The global temperature graph shows a continuous long-term cooling from peak Holocene warmth in the ninth millennium BC until World War I, followed by slow warming during the long mid-century (between the Bolshevik Revolution and 1973 oil crisis) and rapid accelerating warming since the middle 1970s. This does not agree with the peaks in land clearing in Australia — which occurred in the last half of the nineteenth century and the postwar era. However, it is certainly possible that a side-effect of land-clearing in Australia may have been a shift towards land-intensive protein production in the New World, as observed after World War II, for the following reasons:

  • as noted in Richard Seymour’s The Disenchanted Earth: Reflections on Ecosocialism and Barbarism, the US government subsidised beef production massively.
  • it is certainly likely that this demand for animal sources of protein would have been less if labour-intensive plant proteins in the tropics were not rendered so uncompetitive by Australia’s superabundance of grazing land
  • the same increase in beef production took place even in land-poor Europe, based on US government policy with the Marshall Plan
It is also true that the supplanting of chalcophile elements with Australian lithophiles — largely smelted via coal — coincided with global warming accelerating. This also happened immediately after fear of exhaustion of chalcophile “base metals” became acute in the early 1970s.

Thus, even if the raw temperature figures do not imply immediate direct causation, the role of the “Australia shock” in global warming is almost certainly significant.

Secularisation:

Another effect I suspect from the development of Australia’s pre-industrially unusable land is the disappearance of the influence of Christianity, Hinduism and Buddhism on societies previously dominated thereby. Secularisation is a logical effect of any large gain of land, because land is the only factor of production religious institutions can own. Hence, if previously scarce land becomes abundant, religious organisations’ returns will fall dramatically.

The evidence here is highly supportive. The major opening of Australia in the late nineteenth century coincides well with the growth of anti-religion sentiment within the working classes of Europe. The second major “opening” of Australia in the postwar era coincides very well with the complete disappearance of Christianity as a force in Europe, and of Hinduism and Buddhism in land-poor monsoon Asia (where Stalinism and similar ideologies came to dominate). As I noted earlier, even the land-rich New World was by no means exempt from this trend: it simply could never be so land-rich as Australia was.

Also, perhaps more controversially, I can argue that the unpredictability and relative aseasonality of the Australian climate might make religions substantially based upon the very regular (although it must be acknowledged that in places like Gujarat rainy season rainfall is as variable as rainfall in Australia) seasonal cycles of the Levant and monsoon Asia less relevant. Outside the southwestern quarter Australia’s climate is largely controlled by the El Niño Southern Oscillation, which is a highly irregular nonannual cycle with periods as long as seven years and large fluctuations in strength. The climate of the non-ENSO southwestern quarter is vastly less well understood but appears to be most sensitive to acyclical changes in high latitudes like polar ozone depletion and Antarctic pressure and sea surface temperatures. Under such conditions, religious systems developed in Eurasia lose their critical connections to the land and nature upon which their cosmology was based. Because farming in Australia required and requires highly advanced technology to combat ancient soils and a frequently erratic climate, there could never be a replacement religion of a traditional type. Although Australian farmers do speak of attachment to the land, it is extremely important to recognise how unnatural this is because productive crops and livestock require the chalcophile elements so deficient in Australia.

“Australia shock” or European subsidies?

One question I have asked with my putative “Australia shock” is how much its effects are due not to the expansion of land clearing in Australia, but rather to European farm subsidies. Historians such as Jeffrey G. Williamson note that before World War I, although protection of manufacturing was greater than today, agricultural protection was much lower. As noted throughout this post, European and East Asian workers were empowered by nineteenth-century globalisation, and because land was the pillar of ruling class power, subsidising farming became a tool to preserve the influence of farmers against manufacturing workers desiring radical social revolution.

European farm subsidies would logically be expected to have similar global effects to development in Australia. In an artificial manner, they increase the global land supply, and would be expected to reduce returns to land elsewhere in the world, and impoverish backward, land-abundant societies specialising in agriculture. The question is whether European subsidies would have more effect than opening of new land in Australia.

I would argue that this is a debatable question. The critical issue is disincentives to use land efficiently. These are often argued to be a direct result of farm subsidies. Nevertheless, as Wadham Wilson Wood noted in his 1957 Land Utilization in Australia, such disincentives apply equally to superabundant land under a free market, because such land is too cheap and the increase in rent would have to reach extraordinary levels to counter the problem. Politics may be one reason why rent increases have been very limited in rural Australia: Martin Taylor’s Bludgers in Grass Castles from the late 1990s notes how the political influences of pastoralists has made rents “token” in his words. However, limits to productivity on most Australian farmland are severe, with maximum yields for no crop so much as one-half the global maximum, and for some they are as low as one-seventh the global maximum due to the extreme antiquity of Australian soils. This would mean that land values in Australia would never rise nearly so high as in the New World, even under free trade without farm subsidies. Moreover, even if European (and East Asian) farm subsidies do not encourage globally efficient use of land, without the continual opening of new land in Australia up to the twenty-first century the previously noted disincentives would be absent. Hence, the “Australia shock” has itself produced the lavish farm subsidies we see today even in the New World: we cannot entangle it from modern farm subsidies.

Conclusion:

The previously argued points provide substantial evidence for global effects via continued clearing and development of Australia’s superabundant flat land for agriculture. Calling it a “shock” in the sense of Rogowski’s Shocking Contrasts is somewhat inaccurate because the gain of land from opening Australia has occurred over too prolonged a period, but that does not deny its effects.

It is also true that I am uncertain about other effects I expected, chiefly reduced inequality in backward, labour-abundant economies, which I could not relate to the opening of Australia. However, many other predicted effects seem on at least a superficial study to be relatable thereto.

Tuesday, 5 September 2023

Where there cannot be the maximum number of primes

In a few posts from last year, I discussed pentatrigesimal 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).

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:

k 6n 6n+1 6n+2 6n+3 6n+4 6n+5
1
2
2 3 2
2 2
2
2 3
3 3 2
2
2
4 2 3 2
2
5 5 2 3 2 5 2
6 2
2 3 2
7 7 2 7 2 3 2
8 2
2
2 3
9 3 2
2
2
A 2 3 2 5 2 5
B
2 3 2
2
C 2
2 3 2
D
2
2 3 2
E 2 7 2 7 2 3
F 3 2 5 2 5 2
G 2 3 2
2
H
2 3 2
2
I 2
2 3 2
J
2
2 3 2
K 2 5 2 5 2 3
L 3 2 7 2 7 2
M 2 3 2
2
N
2 3 2
2
P 2
2 3 2
Q 5 2 5 2 3 2
R 2
2
2 3
S 3 2
2
2
T 2 3 2 7 2 7
U
2 3 2
2
V 2 5 2 3 2 5
W
2
2 3 2
X 2
2
2 3
Y 3 2
2
2
Z 2 3 2
2
Possible primes 8 8 8 8 8 8

What we see is that whilst there can be ten primes in a span of thirty-five numbers, there can as shown above never be more than eight primes between consecutive multiples of 35. The first occurrence of eight primes between multiples of 35 is between the pentatrigesimal numbers 4L0 and 4LZ, 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.

What I found reading today is that OEIS has actually tabulated the number of possible primes between multiples of base b, as well as the number possible in an arbitrary sequence of length n. I have compared “decades” and “centuries” in all bases up to 35, with sequences serving “centuries” (k00) shaded in grey:

Base Arbitrary Multiple Difference
2 1 1 0
3 2 1 -1
2 4 2 2 0
5 2 2 0
6 2 2 0
7 3 2 -1
8 3 3 0
3 9 4 3 -1
10 4 4 0
11 4 4 0
12 4 4 0
13 5 4 -1
14 5 4 -1
15 5 4 -1
4 16 5 5 0
17 6 5 -1
18 6 6 0
19 6 6 0
20 6 6 0
21 7 5 -2
22 7 7 0
23 7 7 0
24 7 6 -1
5 25 7 7 0
26 7 7 0
27 8 7 -1
28 8 7 -1
29 8 8 0
30 8 7 -1
31 9 8 -1
32 9 9 0
33 10 8 -2
34 10 10 0
35 10 8 -2
6 36 10 10 0
7 49 13 12 -1
8 64 16 16 0
9 81 20 19 -1
10 100 23 23 0
11 121 27 26 -1
12 144 31 30 -1
13 169 37 36 -1
14 196 41 41 0
15 225 46 45 -1
17 289 58 56 -2
18 324 62 62 0
19 361 68 67 -1
20 400 75 75 0
21 441 81 80 -1
22 484 88 87 -1
23 529 95 94 -1
24 576 101 101 0
25 625 109 109 0
26 676 117 116 -1
27 729 124 124 0
28 784 132 131 -1
29 841 141 139 -2
30 900 149 149 0
31 961 158 156 -2

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.

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 4L0 to 4LZ (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.