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 Re: Пентадекатлон мечты
Сообщение24.11.2022, 18:49 
Заслуженный участник


27/06/08
4050
Волгоград
Длинная цепочка с новым самым большим текущим $k$. Полагаю, этот рекорд надолго.
$M(5040)\ge 8$

(Оффтоп)

Код:
n = 1658277738854742457105195396980882611437399218151692458158733458450509754705010871137614747371042624119655109160877126243486792553081613114719723940757564540542094671870
n+3 = 11^(6) * 29^(4) * 59^(2) * 61^(2) * 1860 555610 557587 089396 233041 * 20 628714 972938 069795 923279 331413 (32 digits) * 226 641842 122088 009250 801480 506506 529297 (39 digits) * 11746 015047 886328 978148 952306 240175 715465 321294 385253 (53 digits)

В данный момент все мои мощности сконцентрированы на поиске еще одного пентадекатлона.

 Профиль  
                  
 
 Re: Пентадекатлон мечты
Сообщение24.11.2022, 19:47 


05/06/22
236
VAL в сообщении #1571374 писал(а):
$M(5040)\ge 8$

It gets harder, I find $M(5040) \le 959$.

 Профиль  
                  
 
 Re: Пентадекатлон мечты
Сообщение25.11.2022, 05:10 
Заслуженный участник


27/06/08
4050
Волгоград
Huz в сообщении #1571381 писал(а):
It gets harder, I find $M(5040) \le 959$.

Wow!

 Профиль  
                  
 
 Re: Пентадекатлон мечты
Сообщение25.11.2022, 08:26 
Аватара пользователя


11/12/16
10981
уездный город Н
Huz в сообщении #1571369 писал(а):
So I think it will not be much harder than $D(12,11)$


IMHO.
1. There are no new prime numbers to arrange into patterns. So, the LCM set will be the same.
2. The calculation time of the pattern with the same LCM will increase by 12 times. This is with a naive linear approximation. Rather, the growth will be $12^2$ or so.
3. But even increasing the time by 12 times will lead to disaster for patterns with $LCM=554400$

 Профиль  
                  
 
 Re: Пентадекатлон мечты
Сообщение25.11.2022, 11:50 
Аватара пользователя


29/04/13
5355
Богородский
Объединённая таблица по данным на вчера.

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\node at (4.7,215){\text{1044}};
\node at (28,215){\text{LCM}};
\node at (50,215){\text{3}};
\node at (60,215){\text{4}};
\node at (70,215){\text{5}};
\node at (80,215){\text{6}};
\node at (90,215){\text{7}};
\node at (103,215){\text{Total}};
\node at (118,215){\text{Done}};
\node at (133,215){\text{Work}};
\node at (5.6,205){\text{1.}};
\node at (36,205){\text{554400}};
\node at (50,205){\text{8}};
\node at (60,205){\text{30}};
\node at (70,205){\text{28}};
\node at (104,205){\text{66}};
\node at (90,205){\text{}};
\node at (118,205){\text{1}};
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\node at (5.6,195){\text{2.}};
\node at (35,195){\text{3880800}};
\node at (50,195){\text{8}};
\node at (60,195){\text{46}};
\node at (70,195){\text{60}};
\node at (80,195){\text{28}};
\node at (103,195){\text{142}};
\node at (118,195){\text{14}};
\node at (133,195){\text{?}};
\node at (5.6,185){\text{3.}};
\node at (35,185){\text{6098400}};
\node at (50,185){\text{8}};                       
\node at (60,185){\text{46}};
\node at (70,185){\text{78}};
\node at (80,185){\text{48}};
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\node at (34,175){\text{42688800}};
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\node at (118,175){\text{41}};
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}$

Всего полностью обсчитаны хотя бы однократно $ 1 + 14 + 11 + 41 + 35 + 46 + 152 + 96 + 58 = 454 $ паттерна из $1044$ основных. Количество таких паттернов возросло на 20 по сравнению с предыдущей таблицей.

Конкретика по всем 6 ещё не полностью обсчитанным группам:

(554400-1(66))

Код:
1. b1952:LCM554400-81049-8

(3880800-14(142))

Код:
  1. b133 :LCM3880800-3674745-4
  2. b521 :LCM3880800-1509241-5
  3. b532 :LCM3880800-2567641-5
  4. b542 :LCM3880800-3042841-5
  5. b553 :LCM3880800-2697241-5
  6. b563 :LCM3880800-3755641-5
  7. b592 :LCM3880800-729945-5
  8. b1600:LCM3880800-837945-7
  9. b1601:LCM3880800-3660345-7
10. b1629:LCM3880800-1313145-7
11. b1632:LCM3880800-254745-7
12. b1635:LCM3880800-2018745-7
13. b2102:LCM3880800-681241-8
14. b1637:LCM3880800-2371545-7

(6098400-11(180))

Код:
  1. b112 :LCM6098400-1334745-4
  2. b113 :LCM6098400-3048345-4
  3. b114 :LCM6098400-4761945-4
  4. b116 :LCM6098400-377145-4
  5. b117 :LCM6098400-1233945-4
  6. b118 :LCM6098400-2090745-4
  7. b511 :LCM6098400-3950041-5
  8. b512 :LCM6098400-5663641-5
  9. b520 :LCM6098400-5562841-5
10. b581 :LCM6098400-3105945-5
11. b2134:LCM6098400-378841-8

(42688800-41(226))

Код:
  1. b0   :LCM42688800-30086041-4
  2. b11  :LCM42688800-19502041-4
  3. b41  :LCM42688800-19631641-4
  4. b42  :LCM42688800-3050041-4
  5. b43  :LCM42688800-29157241-4

  6. b121 :LCM42688800-28370745-4
  7. b124 :LCM42688800-11789145-4
  8. b125 :LCM42688800-37896345-4
  9. b129 :LCM42688800-4733145-4
10. b130 :LCM42688800-17786745-4
11. b131 :LCM42688800-30840345-4
12. b139 :LCM42688800-1816569-4   
13. b142 :LCM42688800-14870169-4 
14. b144 :LCM42688800-37449369-4 

15. b530 :LCM42688800-6448441-5
16. b533 :LCM42688800-19502041-5
17. b534 :LCM42688800-34442041-5
18. b540 :LCM42688800-10804441-5
19. b543 :LCM42688800-23858041-5
20. b554 :LCM42688800-19631641-5
21. b555 :LCM42688800-3050041-5
22. b556 :LCM42688800-29157241-5
23. b561 :LCM42688800-38682841-5
24. b570 :LCM42688800-34353945-5
25. b571 :LCM42688800-4718745-5
26. b590 :LCM42688800-24014745-5

27. b1602:LCM42688800-41409945-7
28. b1603:LCM42688800-24828345-7
29. b1606:LCM42688800-8246745-7
30. b1626:LCM42688800-23186745-7
31. b1627:LCM42688800-36240345-7
32. b1630:LCM42688800-19658745-7
33. b1633:LCM42688800-29184345-7
34. b1636:LCM42688800-12602745-7

35. b1836:LCM42688800-4005945-8
36. b1842:LCM42688800-13531545-8    *
37. b1843:LCM42688800-39638745-8
38. b1844:LCM42688800-23057145-8
39. b1874:LCM42688800-23186745-8
40. b1884:LCM42688800-12602745-8
41. b1926:LCM42688800-21148249-8

(1331114400-35(66))

Код:
1. b100 :LCM1331114400-582849945-4
2. b103 :LCM1331114400-945881145-4
3. b108 :LCM1331114400-340829145-4
4. b154 :LCM1331114400-529605369-4
5. b158 :LCM1331114400-650615769-4
6. b163 :LCM1331114400-287584569-4
7. b192 :LCM1331114400-863829369-4
8. b196 :LCM1331114400-500798169-4
9. b201 :LCM1331114400-621808569-4
10. b547 :LCM1331114400-448629241-5
11. b551 :LCM1331114400-569639641-5
12. b576 :LCM1331114400-882485145-5
13. b1033:LCM1331114400-748264441-6
14. b1099:LCM1331114400-761474745-6
15. b1535:LCM1331114400-748264441-7
16. b1610:LCM1331114400-761474745-7
17. b1614:LCM1331114400-882485145-7
18. b1858:LCM1331114400-761474745-8
19. b1862:LCM1331114400-882485145-8
20. b1931:LCM1331114400-1082017849-8
21. b1933:LCM1331114400-476965849-8
22. b1939:LCM1331114400-839997049-8
23. b1981:LCM1331114400-753575449-8    *
24. b1985:LCM1331114400-390544249-8
25. b2005:LCM1331114400-709305817-8    *
26. b2010:LCM1331114400-830316217-8
27. b2014:LCM1331114400-467285017-8
28. b2043:LCM1331114400-1043529817-8
29. b2048:LCM1331114400-680498617-8
30. b2052:LCM1331114400-801509017-8
31. b2115:LCM1331114400-990285241-8
32. b2118:LCM1331114400-385233241-8
33. b2123:LCM1331114400-748264441-8    *
34. b2159:LCM1331114400-327618841-8
35. b2165:LCM1331114400-448629241-8

(8116970400-46(58))

Код:
1. b33  :LCM8116970400-4573365241-4
2. b38  :LCM8116970400-5395691641-4
3. b77  :LCM8116970400-3543605145-4
4. b84  :LCM8116970400-4365931545-4
5. b110 :LCM8116970400-3768432345-4    *
6. b119 :LCM8116970400-7844633145-4    *
7. b165 :LCM8116970400- 196965369-4
8. b170 :LCM8116970400-1019291769-4
9. b175 :LCM8116970400-4273166169-4    *
10. b203 :LCM8116970400-5994801369-4
11. b249 :LCM8116970400-5008202937-4
12. b292 :LCM8116970400-5345443737-4
13. b513 :LCM8116970400-4573365241-5
14. b518 :LCM8116970400-5395691641-5
15. b584 :LCM8116970400-3543605145-5
16. b608 :LCM8116970400-3768432345-5
17. b988 :LCM8116970400-7097678617-6
18. b993 :LCM8116970400-7920005017-6
19. b996 :LCM8116970400-5488457017-6
20. b1008:LCM8116970400-4573365241-6
21. b1013:LCM8116970400-5395691641-6
22. b1044:LCM8116970400-4348538041-6
23. b1112:LCM8116970400-3543605145-6
24. b1150:LCM8116970400-6199980345-6
25. b1153:LCM8116970400-3768432345-6
26. b1496:LCM8116970400-7097678617-7
27. b1501:LCM8116970400-7920005017-7
28. b1514:LCM8116970400-4573365241-7
29. b1544:LCM8116970400-4348538041-7
30. b1623:LCM8116970400-3543605145-7
31. b1866:LCM8116970400-2721278745-8
32. b1871:LCM8116970400-3543605145-8
33. b1906:LCM8116970400-7971863449-8    *
34. b1910:LCM8116970400-3108767449-8    *
35. b1941:LCM8116970400-6812296249-8    *
36. b1951:LCM8116970400-2771526649-8
37. b2016:LCM8116970400-6162938617-8    *
38. b2022:LCM8116970400-6985265017-8    *
39. b2026:LCM8116970400-2122169017-8
40. b2054:LCM8116970400-3843804217-8    *
41. b2059:LCM8116970400-7097678617-8    *
42. b2064:LCM8116970400-7920005017-8    *
43. b2077:LCM8116970400-3751038841-8
44. b2083:LCM8116970400-4573365241-8
45. b2126:LCM8116970400-272337241-8
46. b2135:LCM8116970400-4348538041-8

 Профиль  
                  
 
 Re: Пентадекатлон мечты
Сообщение25.11.2022, 13:42 
Аватара пользователя


11/12/16
10981
уездный город Н
Оценки по времени счета паттернов с различным LCM, в процентах к общему времени.
Оценки очень примерные. В том числе, сделаны в предположении, что -p5e8 ускорит все паттерны в одинаковое количество раз.
$LCM=554400$ - $ 41 \text{\%}$
$LCM=3880800$ - $ 22 \text{\%}$
$LCM=6098400$ - $ 22 \text{\%}$
$LCM=42688800$ - $ 14 \text{\%}$
$LCM=1331114400$ - $ 0.44 \text{\%}$
$LCM=8116970400$ - $ 0.24 \text{\%}$
$LCM=14642258400$ - $ 0.47 \text{\%}$
$LCM=56818792800$ - $ 0.06 \text{\%}$
$LCM=19488845930400$ - $ 0.01 \text{\%}$

Как видно, "основные группы" - это верние четыре.
По тем же оценкам на данный момент времени выполнено 5-6 % работы.

 Профиль  
                  
 
 Re: Пентадекатлон мечты
Сообщение25.11.2022, 14:20 
Заслуженный участник


20/08/14
9900
Россия, Москва
Huz в сообщении #1571068 писал(а):
I noticed also that it can save some time (including in many cases an ispseudoprime check) if you look at $m = p^2qr \pmod{576}$ at the very start, and continue testing only if $m \in \{ 9, 10, 25, 26 \}$. That is enough to verify that the $p$ of $32p$ is not divisible by 2 or 3, and that $32p \equiv \pm 2 \pmod{18}$. (I'm fairly sure I have the right values for $m$, after stepping through a handful of cases.)
I question these 4 values of yours. At least 9 and 10. Let's do the math:
$i=9\cdot16=144, h=\operatorname{round}(i/32)\cdot32=160$, $x=(h+2)/18=9, x\bmod6=3$ - not 1 or 5!
$i=10\cdot16=160, h=\operatorname{round}(i/32)\cdot32=160$, $x=(h+2)/18=9, x\bmod6=3$ - not 1 or 5!
$i=25\cdot16=400, h=\operatorname{round}(i/32)\cdot32=416$, $x=(h-2)/18=23, x\bmod6=5$ - ok.
$i=26\cdot16=416, h=\operatorname{round}(i/32)\cdot32=416$, $x=(h-2)/18=23, x\bmod6=5$ - ok.
The case $x\bmod6=3$ is excluded because 3 is already in 18 and the remaining unknown prime cannot be a 3 (then it would increase the power of 3 here and the divisors would definitely not be 12) and cannot have a remainder 3 modulo 6 (there is only one prime, 3 itself, which is already excluded).
No decisions are missed, but the work is half as slow as possible.

But: we don't need $p^2qr$ if they get further than 7 from $32x$, i.e. 400-408 is unnecessary, as is 424-431.
This leaves only 409-423 modulo 576 acceptable:
Код:
? for(i=0,576-1, n=round(i/32); h=32*n; x=round(h/18); if(abs(h-i)<8 && (n%6==1 || n%6==5) && (x%6==1 || x%6==5), print1(i,", ")))
409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423,
Of all these, can actually be found in $p^2qr$ only such::
Код:
? m=vector(576); forstep(p=1,#m,2, if(p%6==3, next); forstep(qr=1,#m,2, if(qr%6==3, next); x=(p^2*qr)%576; m[x+1]=x)); print(select(x->(x>408 && x<424), Set(m)))
[409, 413, 415, 419, 421]


-- 25.11.2022, 14:34 --

EUgeneUS в сообщении #1571419 писал(а):
The calculation time of the pattern with the same LCM will increase by 12 times. This is with a naive linear approximation. Rather, the growth will be $12^2$ or so.
Для них можно ровно так же взять и ограничить простые, хоть до тех же 5e8. Это будет сильно дольше, но ведь всего один раз посчитать. И тогда интервал квадратичных переборов будет идентичен. А вся разница будет только из-за линейных переборов, которые должны давать примерно линейное время, т.е. всё же примерно в 12 раз, не 144.

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 Re: Пентадекатлон мечты
Сообщение25.11.2022, 16:53 


05/06/22
236
Dmitriy40 в сообщении #1571451 писал(а):
Huz в сообщении #1571068 писал(а):
I noticed also that it can save some time (including in many cases an ispseudoprime check) if you look at $m = p^2qr \pmod{576}$ at the very start, and continue testing only if $m \in \{ 9, 10, 25, 26 \}$. That is enough to verify that the $p$ of $32p$ is not divisible by 2 or 3, and that $32p \equiv \pm 2 \pmod{18}$. (I'm fairly sure I have the right values for $m$, after stepping through a handful of cases.)
I question these 4 values of yours. At least 9 and 10. Let's do the math:
$i=9\cdot16=144, h=\operatorname{round}(i/32)\cdot32=160$, $x=(h+2)/18=9, x\bmod6=3$ - not 1 or 5!

You need to carry the modulus through these calculations: $h \equiv 160 \pmod{576}, x = (h + 2)/18 \implies x \equiv 9 \pmod{32}$. This is not saying that $x$ is divisible by 3. For example $18 \cdot 41 \equiv 162 \pmod{576}$.

Цитата:
But: we don't need $p^2qr$ if they get further than 7 from $32x$, i.e. 400-408 is unnecessary, as is 424-431.

This is a good point though.

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 Re: Пентадекатлон мечты
Сообщение25.11.2022, 22:12 


05/06/22
236
The threshold for large primes for $D(12,11)$ has now reached $10^8$ after just over 44h of calculation. The last 4 hours took advantage of the additional mod 32 check, which made it about 30% faster. I plan to keep working to reduce that threshold for as long as calculations for $D(12,11)$ continue; it is currently reducing it by about 2.8e6 per hour, so I expect to reach $5 \cdot 10^7$ in 2-3 days.

It has found 4 matches for closer investigation so far:
Код:
p=973861969 q= 3 r=  619: 16 256 16  48 12 12 12 12 12 12 12 192  4  8 12
p=237215183 q= 3 r=30869: 24   8 32 192 12 12 12 12 12 12 12  12 16 48 32
p=235289167 q=43 r= 1801:  8 128 32  96 12 12 12 12 12 12 12  12  8 64 16
p=143739307 q=37 r= 4127: 32  16 96  12 12 12 12 12 12 12 12  24  8 32 96

I've also done some preliminary work on the threshold for $D(12,12)$, but I'll probably put that to one side until we're closer to completing $D(12,11)$. The first hour looks like this, where the "305" progress lines show $p, q, r$:
Код:
001 sq12 120402988681658048433948 100000000 141658620564
305 92892284843 (600.00s)
305 75798669647 (1200.00s)
305 65445536251 2 13 (1800.00s)
305 56868941989 2 11 (2399.99s)
305 50252884793 3 7 (2999.99s)
305 44544175211 5 (3599.99s)

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 Re: Пентадекатлон мечты
Сообщение26.11.2022, 06:02 
Аватара пользователя


29/04/13
5355
Богородский
Yadryara в сообщении #1571434 писал(а):
Всего полностью обсчитаны хотя бы однократно $ 1 + 14 + 11 + 41 + 35 + 46 + 152 + 96 + 58 = 454 $ паттерна из $1044$ основных.

Нынче уже $1 + 15 + 13 + 41 + 35 + 47 + 152 + 96 + 58 = 458$.

Полностью обсчитаны хотя бы однократно 47 из 58 паттернов с шагом 8116970400. Возможно, лучше указать явно оставшиеся 11:

b207 :LCM8116970400-1131705369-4
b213 :LCM8116970400-1954031769-4
b253 :LCM8116970400-145106937-4
b301 :LCM8116970400-1304674137-4
b641 :LCM8116970400-196965369-5
b646 :LCM8116970400-1019291769-5
b1048:LCM8116970400-1916990041-6
b1107:LCM8116970400-2721278745-6
b1193:LCM8116970400-2628513369-6
b1197:LCM8116970400-196965369-6
b1202:LCM8116970400-1019291769-6

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 Re: Пентадекатлон мечты
Сообщение26.11.2022, 11:54 
Аватара пользователя


11/12/16
10981
уездный город Н
Huz
Are you considering using a "two-stage booster" for patterns with LCM=554400?
That is, a further decrease in the threshold of simple ones is already individual for patterns.

Argumentation:
1. With the current value of the threshold, the calculation time will be:
1.1 Less than a day for patterns with LCM=42688800
1.2 Few days for patterns with LCM=6098400 and 3880800

2. But pattern calculation time with LCM=554400 continues to be problematic.

3. Perhaps the complicated procedure for starting programs will be difficult for some participants. However, we can first close the LCM=554400 pattern issue for ranges that are not allocated to participants with such difficulties.

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 Re: Пентадекатлон мечты
Сообщение26.11.2022, 17:36 


05/06/22
236
EUgeneUS в сообщении #1571545 писал(а):
Are you considering using a "two-stage booster" for patterns with LCM=554400?

Sorry, I don't know what sort of "two-stage booster" you mean.

I am currently testing a pattern (b1619) having LCM-554400 with "-p5e7". It currently looks like it will complete in under 3 days (probably closer to 2 days), not long after the threshold itself reaches 5e7 - after 23h the main $p^2$ allocation has reached $p=9467$ and $p$ is growing by about 1000 every 10 minutes, still accelerating slightly. My best guess is that growth will stabilize at between 1200 and 1500 per 10 minutes, then transition to linear search somewhere around $40000 < p < 60000$ before it starts to accelerate again. That's the speed on my computer, of course, but the slowest computer among the contributors is no worse than half as fast.

Цитата:
Perhaps the complicated procedure for starting programs will be difficult for some participants.

This is perhaps a bigger problem - I originally wrote the code imagining it would only be used by people with the resources to compile it themselves, and with the inclination to inspect and modify the source. I find myself in a rather different world. Unfortunately I have recently also been unable to reach CorporalTermit, who was making the Windows builds, and I do not know how long they may remain unavailable.

Perhaps the most useful thing someone could do right now is work out an algorithmic way to estimate the optimal value of -g to reasonable accuracy, given the pattern and the "-p" threshold. If we have that we can either build it into pcoul or provide it separately, eg as a Windows batch file. Right now the only way I know to estimate it is with a time-consuming process involving multiple manual bisections to find the optimal prime at which to transition from recursion to linear search.

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 Re: Пентадекатлон мечты
Сообщение26.11.2022, 18:22 
Заслуженный участник


20/08/14
9900
Россия, Москва
Yadryara в сообщении #1571529 писал(а):
Возможно, лучше указать явно оставшиеся 11:
Давайте уже добьём их:
Код:
T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b1202 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b1202 *RT*
17^5 2^2.3 . 2 3.5^2 2^5 7 2.3^2 11^5 2^2.5 3: 10296 / 433841
367 coul(12, 11): recurse 282393630, walk 282402443, walkc 640314738 (1329.32s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b1197 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b1197 *RT*
23^5 2^2.3 11^5 2 3.5^2 2^5 7 2.3^2 . 2^2.5 3: 24887 / 95705
367 coul(12, 11): recurse 282393630, walk 282402443, walkc 640314903 (1308.58s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b1193 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b1193 *RT*
2 3 2^2 5 2.3 7^3 2^3 3^2 2.5^2 . 2^2.3
367 coul(12, 11): recurse 282393630, walk 282402443, walkc 640314410 (1263.03s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b1107 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b1107 *RT*
11^5 2^2.3 7 2.5^2 3 2^5 13^5 2.3^2 5 2^2.7 3: 1594340 / 1659048
367 coul(12, 11): recurse 282313166, walk 282411257, walkc 640271443 (1091.51s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b1048 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b1048 *RT*
3 2^2 5 2.3^2 7 2^5 3 2.5^2 17^5 2^2.3 11^5: 210049 / 433841
367 coul(12, 11): recurse 282313166, walk 282411257, walkc 640271627 (1292.33s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b646 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b646 *RT*
2^2.3 17^5 2 3.5^2 2^5 7 2.3^2 11^5 2^2.5 3 2: 99549 / 433841
367 coul(12, 11): recurse 282313166, walk 282411649, walkc 640271810 (1324.28s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b641 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b641 *RT*
2^2.3 11^5 2 3.5^2 2^5 7 2.3^2 23^5 2^2.5 3 2: 40024 / 95705
367 coul(12, 11): recurse 282313166, walk 282411649, walkc 640271966 (1306.68s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b301 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b301 *RT*
37^5 2 3 2^5 5 2.3^2 7 2^2 3 2.5^2 11^5: 6121 / 8882
367 coul(12, 11): recurse 282313166, walk 282411257, walkc 640271403 (1317.09s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b253 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b253 *RT*
7 2 3 2^5 5 2.3^2 17^5 2^2.7 3 2.5^2 11^5: 109557 / 433841
367 coul(12, 11): recurse 282313166, walk 282411257, walkc 640271904 (1112.43s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b213 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b213 *RT*
13^5 2 3.5^2 2^5 . 2.3^2 7 2^2.5 3 2 11^5: 1629635 / 1659048
367 coul(12, 11): recurse 282393630, walk 282402443, walkc 640314287 (1295.38s)

T:\M12minimal\Hugo>pcoul.exe -x1e22 -p1e8 -f11 -g9 -v -b207 12 11
001 pcoul(12 11) -p100000000 -f11 -g9 -x10000000000000000000000 -b207 *RT*
19^5 2 3.5^2 2^5 11^5 2.3^2 7 2^2.5 3 2 .: 25913 / 248775
367 coul(12, 11): recurse 282393630, walk 282402443, walkc 640314143 (1294.62s)


-- 26.11.2022, 18:36 --

Huz
Implementing the two-step acceleration process does not require modification of the pcoul code! It is sufficient to organize it with third-party software, just like sq12.c. The only difference is that the constraint is not checked and enforced for all patterns, but only for one particular pattern. Since the numbers to be checked are big, you can check by linear search, which will be very fast (e.g., for patterns with LCM=554400 checking a prime number about 1e8 requires only two iterations of linear search for every possible place in the pattern). Accordingly, it is easy to reduce the -pZ threshold to a few million, which would reduce the time to check the pcoul of such a pattern to a dozen hours or less.
Again, no modification of pcoul is required.

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 Re: Пентадекатлон мечты
Сообщение26.11.2022, 20:36 


05/06/22
236
Dmitriy40 в сообщении #1571568 писал(а):
Implementing the two-step acceleration process does not require modification of the pcoul code! It is sufficient to organize it with third-party software, just like sq12.c. The only difference is that the constraint is not checked and enforced for all patterns, but only for one particular pattern. Since the numbers to be checked are big, you can check by linear search, which will be very fast (e.g., for patterns with LCM=554400 checking a prime number about 1e8 requires only two iterations of linear search for every possible place in the pattern). Accordingly, it is easy to reduce the -pZ threshold to a few million, which would reduce the time to check the pcoul of such a pattern to a dozen hours or less.

Ah, so the idea is for a variant of sq12 to check only those $p^2qr$ for which the nearest $n_{32}$ has the appropriate value $\pmod{554400}$? I can see that that could give some benefit. However I am, as always, nervous about how well debugged something with such a specific application would be. And if LCM=554400 patterns can already be completed in 48 hours (and improving) without this, the value is limited at least until we move on to $D(12,12)$.

My instinct is that, within the ecosystem of my code, something working on a specific pattern would probably belong inside pcoul. But I will think further on this.

(later) Oh, you don't mean that - I think rather that you mean to avoid generating $p^2qr$ the way sq12 does it. But in that case it sounds not at all different from what pcoul does itself.

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 Re: Пентадекатлон мечты
Сообщение26.11.2022, 21:07 
Заслуженный участник


20/08/14
9900
Россия, Москва
Huz
Answer a simple question for a pattern like b1952: how many times will the second level of recursion be run and therefore how many times will it check for prime numbers greater than 1e7 (and up to 1e8)?
Now pay attention: you can check all such prime numbers once by direct substitution in place of the second level of recursion (or for safety - in all possible places of the pattern) and without touching anything else run linear check (after CRT) to see if there are any solutions. Since we did not substitute a prime number from the first level of recursion, we will of course need to iterate more, but only about 170 times ($13^2$). This is easy to estimate: the number of iterations of the linear search would be $10^{22}/554400/(10^7)^2=180$, a total of 180 for each prime number on the second level of recursion. And as the substituted prime increases (up to 1e8), the number of iterations will drop even further, down to 2.
By checking all prime numbers from 1e7 to 1e8 in this way, we can limit the second level of recursion to 1e7 instead of a total of 1e8 for all.
By repeating this check for all possible places in the pattern, we will limit all of them to 1e7 instead of 1e8.
At a 2e5/s linear check speed, checking this entire 1e7-1e8 range for one particular pattern and one place in it will take about half an hour. Checking even all 7 places (not to check where what level of recursion will be when pcoul works) in a pattern will take 4 hours. And you can run pcoul with -p1e7 for that particular pattern. I hope it is obvious that the difference in running time of pcoul with -p1e8 and -p1e7 significantly exceeds the cost of 4 hours. And of course the threshold 1e7 is just for example, you can really choose a smaller one, our tests above show optimality somewhere around 1e6-4e6.
And the whole point of this action is exactly in single check of such simple ones, albeit 170 times longer each time, but once and not as long as the second (third and so on) level of recursion will be run.
And this check can be done separately, not in pcoul, just like you already do with sq12. And here we have a file, say, sq12-b1952.c, which checks the constraint not for all patterns, but only for b1952.

PS. Я не знаю как ещё объяснять ... По моему проще уже просто код написать. Собственно на PARI он уже был выше, там же всё просто за парой исключений (select для получения индексов возможных мест, да и всё в общем).

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