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[Huz]

Dmitriy40 в сообщении #1576983 писал(а):

Huz
Is there any way to get pcoul to check the pattern without recompiling?
2.53 . 2^2.3 7 2.5^2 3 2^5 11 2.3^2 5 2^2.7 3 [sq=1]

I'm looking at implementing this, but it appears that the 11 is incompatible with the square so it is still rejecting it:

% ./pcoul -x120402988681658048433948 -I"2.53 . 2^2.3 7 2.5^2 3 2^5 11 2.3^2 5 2^2.7 3" 12 12
001 pcoul(12 12) -x120402988681658048433948
error injecting 11^1 at v_7
% 

Do you agree that this is an invalid pattern? If you have an alternative pattern that demonstrates what you intended to achieve that you think should be valid, I can test whether my implementation will work.

[Dmitriy40]

Huz в сообщении #1579756 писал(а):

Do you agree that this is an invalid pattern?

I agree, 2.53 is unacceptable by modulo 11, but it was not a question of modulo acceptability, but how to get pcoul to check patterns with placed large primes. I was hoping check by pcoul would be faster and more versatile than check by PARI, it would make it much easier to reduce the -p threshold for the largest primes (but the real speed has yet to be discovered).

To check correctness, you can use, for example, the recently found chain
38035281*2639713673^2:265033195588524939489926041: 16, 32, 16, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 64,192, valids=10, maxlen=10
corresponding to the pattern D12n10-b136
2^2 5 2.3^2 7^2 2^5 3.12678427 2.5^2 . 2^2.3 . [sq=1]
which turns into sq=1 because of the addition of 12678427 and should check quadratically.

-- 01.02.2023, 21:05 --

Dmitriy40 в сообщении #1579779 писал(а):

I was hoping check by pcoul would be faster and more versatile than check by PARI, it would make it much easier to reduce the -p threshold for the largest primes (but the real speed has yet to be discovered).

Generally speaking, this question has lost its relevance: after I wrote and Ferma test for $p<2^{64}$ and KTO (up to $2^{128}$) and generating primes (up to $2^{64}$), the speed of checking large prime is already limited to them and by using assembler and AVX she most likely exceeds the speed of C program.

[Huz]

Dmitriy40 в сообщении #1579779 писал(а):

To check correctness, you can use, for example, the recently found chain 38035281*2639713673^2

Thanks, that was helpful.

Цитата:

Generally speaking, this question has lost its relevance

Well if it would have been useful once, it is likely to be useful again - I've occasionally wanted something similar myself, but never got around to adding it.

As well as allowing a complete pattern to be specified with "-I", I would also like to add the option to specify one or more modular constraints, eg "-m53=0" would specify that the first value $v_0$ should honour $v_0 \equiv 0 \pmod{53}$. The -I option will require that all forced primes are specified, while -m can be used more generally. However so far it is proving to be more difficult to add: some parts of the code assume that such modular constraints can only have been added by an allocation.

[Dmitriy40]

Huz
I noticed a strange thing: the fifth degrees of the prime are enumerated for each substituted prime squared. But this is completely unnecessary, it is enough to search them once for each place and then limit their search not to the number specified in -p, but literally the first hundreds. Here is an example of the log:

001 pcoul(12 13) -p200000 -f13 -g10 -x600000000000000000000000000 -b198 *RT*
305 3.154769^5 2^2.7 5.11^2 2.3^2 13^5 2^5 3 2.5^2 7^2 2^2.3 8237^2 2 3^2.5 (587.16s)

Here you can see that $154769^5$ began to check for the substituted $8237^2$, and obviously for all others (can see it on the screen). That is, not only are the squared primes being substituted, but so many fifth powers are also being substituted, although for all $p>\sqrt[5]{6\cdot10^{26}/15850052618400}=520$ they can be checked exactly once and then only go through up to $520$ instead of $200000$. This will greatly speed up the calculations for small -p's (-W's).

[EUgeneUS]

По поиску более меньшей 12-14.

Поименуем группы "перспективных паттернов", как на рисунке ниже:


"Группа А". Закончен расчет диапазона 0-7e31. Диапазоны 7-14e31 и 14-21e31 в расчете к DemIS'а. Считаются сразу оба диапазона, так что финал будет сразу по обоим.
"Группа Б". В этой группе находится минимальная известная цепочка. Но эта группа подробно исследовалась Дмитрием. Пока не рассчитывается.
"Группа В". Закончен расчет диапазона 0-7e31. Диапазоны 7-14e31 в расчете у меня. Частично завершен, частично в работе.
"Группа Ж". Закончен расчет диапазона 0-7e31. Диапазоны 7-14e31 в расчете у меня. Считается в один поток.
"Группы Г, Д, Е".... Это проблема. С одной стороны, считать с таким же ограничением на простые в больших степенях (-p500) - это очень надолго. С другой стороны, у меня нет аргументов, что это "менее перспективные паттерны", чем другие группы с количеством проверяемых мест 11. Любые мысли о расчете этих паттернов - приветствуются.

Всё считается с ограничением на простые в больших степенях: -p500.
В рассчитанных паттернах\диапазонах цепочек не найдено.

Пока цель такая:
1. Рассчитать "Группы А, В и Ж" до 21e31.
2. Рассчитать "Группу Б" до 21e31.
3. И что-то нужно будет делать с "Группами Г, Д, Е"....

[=SSN=]

EUgeneUS в сообщении #1580514 писал(а):

Пока цель такая:

4. Потратить ещё 100500 МВтч электроэнергии на поиски никому не нужной последовательности бессмысленных цифр..

А.С.Грибоедов, "Горе от ума", часть 2-я..

[EUgeneUS]

=SSN= в сообщении #1580515 писал(а):

4. Потратить ещё 100500 МВтч электроэнергии

Чушь не нужно писать.
Всё посчитано, 250 кВт-час за месяц, за 700 рублей. А не "100500 МВтч" за "сотни нефти"

[=SSN=]

EUgeneUS в сообщении #1580516 писал(а):

Всё посчитано...

Отнюдь..

Вам ещё ... что-то нужно будет делать с "Группами Г, Д, Е,... Т,А,М".... до 999e999..

[Dmitriy40]

=SSN=
Поиск наибольшего известного простого числа или триллионов цифр числа пи - не более осмысленно.
Лично мне например профит в повышении собственной квалификации (программы на ассемблере, вот недавно например тест простоты Ферма написал, оказалось совсем несложно) и просто интересно. И это точно стоит затраченных лично мною денег на электричество и аппаратуру.

[EUgeneUS]

=SSN= в сообщении #1580518 писал(а):

Отнюдь..

Вам ещё ... что-то нужно будет делать с "Группами Г, Д, Е,... Т,А,М".... до 999e999..

Вы опять и снова пишите чушь.
Более 250 кВт-час за месяц мои железки не сожрут, чтобы там не делать с группами "ГДЕ" или "ЁЖЗИК".

[Huz]

Dmitriy40 в сообщении #1580476 писал(а):

Huz
I noticed a strange thing: the fifth degrees of the prime are enumerated for each substituted prime squared. But this is completely unnecessary, it is enough to search them once for each place and then limit their search not to the number specified in -p, but literally the first hundreds. ... This will greatly speed up the calculations for small -p's (-W's).

I understand your point, but it would not be particularly easy to add. I am not convinced that it would be a huge speed improvement, though - checks where all the divisors have already been accounted for are normally very fast.

[Dmitriy40]

Huz в сообщении #1580545 писал(а):

I am not convinced that it would be a huge speed improvement,

Make the -PXXX switch to limit primes to degrees greater than the second (i.e. the fifth), or just remove the fifth degree enumeration, run it and compare time. Maybe not twice, but there should be a speed gain. Especially for fairly small -P/-W's, like the ones I have above.

[Huz]

Dmitriy40 в сообщении #1580551 писал(а):

Make the -PXXX switch to limit primes to degrees greater than the second (i.e. the fifth), or just remove the fifth degree enumeration, run it and compare time. Maybe not twice, but there should be a speed gain. Especially for fairly small -P/-W's, like the ones I have above.

You're right, the difference is bigger than I expected if I hack the code to return immediately when asked to consider working on a prime power that would leave the remaining tau equal to 1:

# without hack
001 pcoul(12 13) -p200000 -f13 -g10 -x60000000000000000000000000 -b198
367 coul(12, 13): recurse 44878407, walk 71984211, walkc 56675032 (117.99s)
# with hack
001 pcoul(12 13) -p200000 -f13 -g10 -x60000000000000000000000000 -b198
367 coul(12, 13): recurse 44878407, walk 44889726, walkc 56675032 (78.53s)

I'll have to think further about how to implement that.

[Dmitriy40]

Huz
Thanks for the test.
I think you can do it after you do -W, it's the same as it, only with a different degree.
And inside the code to make the second threshold limit, for prime in the maximum degree searched (I do not think that you should do for other degrees, although it is not difficult to make an array, but whether there will be a strong gain for other degrees is still a question) and set it in min(-p, sqrt[n](-x)/LCM), in the second case by brute force from sqrt[n](-x)/LCM to sqrt[n](-x/2) with check exactly as in -W.
Whether you need a separate key for this and what kind - I'm not sure, at your discretion. I think it should be more like -W than -p.

-- 07.02.2023, 12:29 --

By the way, this would loosen (and greatly) the restrictions on -W. You may not have to redo its work either ...

[Huz]

Dmitriy40
If I do it after -W, then we have already selected the pattern; however in this example it would be preferable to test all cases of an element of the form $3p^5$ just once, rather than doing it once per pattern. I agree doing it after selecting the pattern makes lives easier.

I may be misunderstanding the phrase "maximum degree", is that intended to be the same as "maximum power"? Because the maximum power would be $p^{11}$ here, so I don't understand what you mean by "for prime in the maximum degree searched". (The variables in your formula are also not clear to me, but I'm confident I can work out what is needed there.)

In any case I already have code that removes all restrictions on -W, so that ship has sailed - I have a full run going for $D(48,10)$ with -W1e5 right now. I am currently working on automatic calibration (using timings to determine the switch from recursion to linear search instead of the user-supplied "gain") and planned to release a new version when that was working.