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Message boards : 321 Prime Search : Next Prime

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Paul Underwood
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Joined: 14 Jul 08
Posts: 66
ID: 25545
Credit: 3,482,191
RAC: 0
321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 43986 - Posted: 26 Nov 2011 | 23:32:47 UTC
Last modified: 26 Nov 2011 | 23:36:57 UTC

Hi,

below is a simple statistical calculation. PG is very close to the mean expected prime n: 8172825.9871397

1 0.0000000 2 2.0000000 3 1.5000000 4 1.3333333 6 1.5000000 7 1.1666667 11 1.5714286 18 1.6363636 34 1.8888889 38 1.1176471 43 1.1315789 55 1.2790698 64 1.1636364 76 1.1875000 94 1.2368421 103 1.0957447 143 1.3883495 206 1.4405594 216 1.0485437 306 1.4166667 324 1.0588235 391 1.2067901 458 1.1713555 470 1.0262009 827 1.7595745 1274 1.5405079 3276 2.5714286 4204 1.2832723 5134 1.2212179 7559 1.4723413 12676 1.6769414 14898 1.1752919 18123 1.2164720 18819 1.0384042 25690 1.3651097 26459 1.0299338 41628 1.5733021 51387 1.2344336 71783 1.3969097 80330 1.1190672 85687 1.0666874 88171 1.0289892 97063 1.1008495 123630 1.2737088 155930 1.2612634 164987 1.0580838 234760 1.4229000 414840 1.7670813 584995 1.4101702 702038 1.2000752 727699 1.0365522 992700 1.3641629 1201046 1.2098781 1232255 1.0259848 2312734 1.8768307 3136255 1.3560812 4235414 1.3504686 6090515 1.4379976 av 1.3418941 std.dev 0.2920128 std.error 0.0386780378 -95% 1.2645379986 7701687.64868202 95% 1.4192501497 8643964.32559737 mean 8172825.9871397


Paul

Paul Underwood
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Joined: 14 Jul 08
Posts: 66
ID: 25545
Credit: 3,482,191
RAC: 0
321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 62191 - Posted: 1 Feb 2013 | 22:45:11 UTC - in response to Message 43986.

av 1.3418941
std.dev 0.2920128
std.error 0.0386780378
-99.70% 2837301.30994368
-95.00% 4615809.53567568
-68.00% 6394317.76140769
average 8172825.9871397
68.00% 9087584.31966443
95.00% 11729842.4386037
99.70% 13508350.6643357

Gives a better picture of what is expected. But this is still a crude Gaussian normal curve for 3*2^n-1. based on the last prime which was a little bigger than expected. If some one can do an expectation based on the Poisson distribution and post it here I am sure we would all be grateful,

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Found 1 prime in the 2018 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,805,841)Cullen LLR Amethyst: Earned 1,000,000 credits (1,305,599)ESP LLR Ruby: Earned 2,000,000 credits (2,085,950)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,050,279)PPS LLR Ruby: Earned 2,000,000 credits (2,149,793)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,493,571)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,072,856)TRP LLR Ruby: Earned 2,000,000 credits (2,066,087)Woodall LLR Amethyst: Earned 1,000,000 credits (1,293,758)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,151)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,291,817)GFN Emerald: Earned 50,000,000 credits (55,143,105)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 62196 - Posted: 2 Feb 2013 | 1:37:52 UTC - in response to Message 62191.
Last modified: 2 Feb 2013 | 2:31:51 UTC

To calculate a Poisson distribution you first find the average; 1.341894077
Poisson random variable must be an integer, so you need to divide the range into intervals. I used 0.1 but can be anything.
Then you have to find an average rate of success for each interval, starting with 1 to 1.1. Do to average what you did to range: (X-1)*10
Using spreadsheet formula =POISSON(value,3.41894077) where value is 0,1,2,3.. corresponding to range 1 to 1.1, 1.1 to 1.2, 1.2 to 1.3,..
You end up with % chance to be in some range:
Range ; next n ; % chance
1.0 to 1.1 ; 6090515 to 6699567 ; 3.27%
1.1 to 1.2 ; 6699567 to 7308618 ; 11.20%
1.2 to 1.3 ; 7308618 to 7917670 ; 19.14%
1.3 to 1.4 ; 7917670 to 8526721 ; 21.81%
1.4 to 1.5 ; 8526721 to 9135773 ; 18.64%
1.5 to 1.6 ; 9135773 to 9744824 ; 12.75%
1.6 to 1.7 ; 9744824 to 10353876; 7.26%
1.7 to 1.8 ;10353876 to 10962927; 3.55%
1.8 to 1.9 ;10962927 to 11571979; 1.52%
1.9 to 2.0 ;11571979 to 12181030; 0.58%
2.0 to 2.1 ;12181030 to 12790082; 0.2%
2.1 to 2.2 ;12790082 to 13399133; 0.06%
2.2 to 2.3 ;13399133 to 14008185; 0.02%
____________

Profile Roger
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Joined: 27 Nov 11
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Found 1 prime in the 2018 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,805,841)Cullen LLR Amethyst: Earned 1,000,000 credits (1,305,599)ESP LLR Ruby: Earned 2,000,000 credits (2,085,950)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,050,279)PPS LLR Ruby: Earned 2,000,000 credits (2,149,793)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,493,571)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,072,856)TRP LLR Ruby: Earned 2,000,000 credits (2,066,087)Woodall LLR Amethyst: Earned 1,000,000 credits (1,293,758)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,151)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,291,817)GFN Emerald: Earned 50,000,000 credits (55,143,105)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 62341 - Posted: 7 Feb 2013 | 5:54:31 UTC - in response to Message 62196.

I was a bit unsatified with the Poisson Distribution, so decided to graph the distribution by:
1. Sorting the ratio of prime finds. The list for k < 300 is given here: http://www.prothsearch.com/riesel2.html
2. Graphing the distribution by giving each ratio an equal weight. This is the blue line in the graph:

3. Finding line of best fit. That is the red line in the above graph. The equation I got was:
1-32.122*e^(-3.395*X), where X = last prime * n

This result is satisfying because the cumulative distribution of the gaps between the values of a Poisson process should be governed by an exponential distribution:
http://primes.utm.edu/notes/faq/NextMersenne.html

Running the numbers:
Range ; next n ; % chance
1.0 to 1.1 ; 6090515 to 6699567 ; 31.02%
1.1 to 1.2 ; 6699567 to 7308618 ; 22.09%
1.2 to 1.3 ; 7308618 to 7917670 ; 15.73%
1.3 to 1.4 ; 7917670 to 8526721 ; 11.20%
1.4 to 1.5 ; 8526721 to 9135773 ; 7.98%
1.5 to 1.6 ; 9135773 to 9744824 ; 5.68%
1.6 to 1.7 ; 9744824 to 10353876; 4.05%
1.7 to 1.8 ;10353876 to 10962927; 2.88%
1.8 to 1.9 ;10962927 to 11571979; 2.05%
1.9 to 2.0 ;11571979 to 12181030; 1.46%
2.0 to 2.1 ;12181030 to 12790082; 1.04%
2.1 to 2.2 ;12790082 to 13399133; 0.74%
2.2 to 2.3 ;13399133 to 14008185; 0.53%
2.3 to inf ;greater than 14008185; 1.31%

You can see the new distribution is much thicker at the start and in the tail. I plan to also try this out for other k.
Bottom line is crunch early, crunch often!
____________

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Discovered 4 mega primesEliminated 3 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage321 LLR Sapphire: Earned 20,000,000 credits (34,352,250)Cullen LLR Sapphire: Earned 20,000,000 credits (25,424,693)ESP LLR Sapphire: Earned 20,000,000 credits (22,668,198)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (21,044,302)PPS LLR Emerald: Earned 50,000,000 credits (67,163,078)PSP LLR Sapphire: Earned 20,000,000 credits (23,462,639)SoB LLR Emerald: Earned 50,000,000 credits (58,594,951)SR5 LLR Emerald: Earned 50,000,000 credits (50,308,578)SGS LLR Sapphire: Earned 20,000,000 credits (22,597,792)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Emerald: Earned 50,000,000 credits (51,404,601)Woodall LLR Sapphire: Earned 20,000,000 credits (24,573,411)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (4,024,795)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (504,377,255)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Emerald: Earned 50,000,000 credits (69,229,896)GFN Double Gold: Earned 500,000,000 credits (580,674,019)PSA Double Gold: Earned 500,000,000 credits (530,514,240)
Message 62345 - Posted: 7 Feb 2013 | 9:48:18 UTC

With n ~9,37m, aren't we a bit overdue with next 321 prime?

3·2^7033641+1 (321) 2011/02
3·2^6090515-1 (321) 2010
3·2^5082306+1 (321) 2009
3·2^4235414-1 (321) 2008

I was thinking to swich to longer subproject during server move/outage.
321 might not be long enough for fast computers but still quite appealing.
____________
My stats
Badge score: 1*1 + 5*2 + 8*9 + 9*6 + 12*3 = 173

Paul Underwood
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Joined: 14 Jul 08
Posts: 66
ID: 25545
Credit: 3,482,191
RAC: 0
321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 62358 - Posted: 7 Feb 2013 | 18:42:07 UTC
Last modified: 7 Feb 2013 | 18:52:08 UTC

Thanks for your statistics, Roger.

Remember that this is for half of 321 Prime Search. Not only are we due a prime of the form 3*2^n-1, there is also the chance of finding a prime of the form 3*2^n+1. PrimeGrid is at about 9,369,596 bits. All the more reason to crunch for this sub-project -- a top20 prime is nigh!

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Joined: 27 Nov 11
Posts: 1054
ID: 120786
Credit: 253,637,478
RAC: 9,427
Found 1 prime in the 2018 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,805,841)Cullen LLR Amethyst: Earned 1,000,000 credits (1,305,599)ESP LLR Ruby: Earned 2,000,000 credits (2,085,950)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,050,279)PPS LLR Ruby: Earned 2,000,000 credits (2,149,793)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,493,571)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,072,856)TRP LLR Ruby: Earned 2,000,000 credits (2,066,087)Woodall LLR Amethyst: Earned 1,000,000 credits (1,293,758)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,151)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,291,817)GFN Emerald: Earned 50,000,000 credits (55,143,105)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 62697 - Posted: 16 Feb 2013 | 23:48:04 UTC - in response to Message 62358.
Last modified: 16 Feb 2013 | 23:51:10 UTC

Doing the exercise for the 3*2^n+1 case gives equation of the form 1-5.152*e^(-1.630*X), where X = last prime * n

Running the numbers:
Range ; next n ; % chance
1.0 to 1.1 ; 7033641 to 7737005 ; 14.29%
1.1 to 1.2 ; 7737005 to 8440369 ; 12.90%
1.2 to 1.3 ; 8440369 to 9143733 ; 10.96%
1.3 to 1.4 ; 9143733 to 9847097 ; 9.31%
1.4 to 1.5 ; 9847097 to 10550462; 7.91%
1.5 to 1.6 ;10550462 to 11253826; 6.72%
1.6 to 1.7 ;11253826 to 11957190; 5.71%
1.7 to 1.8 ;11957190 to 12660554; 4.85%
1.8 to 1.9 ;12660554 to 13363918; 4.12%
1.9 to 2.0 ;13363918 to 14067282; 3.50%
2.0 to 2.1 ;14067282 to 14770646; 2.97%
2.1 to 2.2 ;14770646 to 15474010; 2.53%
2.2 to 2.3 ;15474010 to 16177374; 2.15%
2.3 to inf ;greater than 16177374;12.12%

When we add the 3*2^n+1 and 3*2^n-1 probabilities for up and coming ranges we get:
Range ; % chance
9.37 to 9.4M ; 0.5%
9.4 to 9.6M ; 4.46%
9.6 to 9.8M ; 4.15%
9.8 to 10M ; 3.87%
10 to 10.5M ; 8.57%
10.5 to 11M ; 7.24%
11 to 11.5M ; 6.14%
11.5 to 12M ; 5.24%
12 to 12.5M ; 4.49%
12.5 to 13M ; 3.87%
13 to 13.5M ; 3.35%
13.5 to 14M ; 2.90%
14 to 14.5M ; 2.53%
14.5 to 15M ; 2.21%
15 to 15.5M ; 1.93%
15.5M to inf ; 14.78%

Note that these probabilities don't take account of the fact prime was not found < 9.37M.
When we normailise (by making the remaining range add up to 100% chance for both +/- cases) we get:
Range ; next n ; % chance
9.37 to 9.4M ; 1.67%
9.4 to 9.6M ; 14.83%
...

All numbers to 25M are loaded in the Boinc Database. There is a table with only 321 work up to 25M.
If someone could run a Database query for how many n there are to be checked in the up and coming ranges we could see the 1 in X chance for each WU of finding a huge prime!
____________

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Joined: 27 Nov 11
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Found 1 prime in the 2018 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,805,841)Cullen LLR Amethyst: Earned 1,000,000 credits (1,305,599)ESP LLR Ruby: Earned 2,000,000 credits (2,085,950)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,050,279)PPS LLR Ruby: Earned 2,000,000 credits (2,149,793)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,493,571)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,072,856)TRP LLR Ruby: Earned 2,000,000 credits (2,066,087)Woodall LLR Amethyst: Earned 1,000,000 credits (1,293,758)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,151)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,291,817)GFN Emerald: Earned 50,000,000 credits (55,143,105)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 63467 - Posted: 13 Mar 2013 | 13:18:10 UTC - in response to Message 62697.

Thanks to JimB for querying the database for the number of raw candidates in the up and coming ranges!
Adding the 3*2^n+1 and 3*2^n-1 normalised probabilities (so search from here adds up to 100% chance for each +/-):

Range ; candidates ; % chance ; 1 in X chance of prime per candidate
9.4 to 9.6M ; 17462 ; 14.98% ; 116,601
9.6 to 9.8M ; 17528 ; 13.68% ; 128,133
9.80 to 10M ; 17402 ; 12.51% ; 139,144
10 to 10.5M ; 43550 ; 26.84% ; 162,287
10.5 to 11M ; 43627 ; 21.62% ; 201,790
11 to 11.5M ; 43365 ; 17.52% ; 247,450
11.5 to 12M ; 43468 ; 14.29% ; 304,089
12 to 12.5M ; 43590 ; 11.73% ; 371,481
12.5 to 13M ; 43264 ; 9.69% ; 446,296
13 to 13.5M ; 43761 ; 8.06% ; 542,982
13.5 to 14M ; 43476 ; 6.74% ; 644,860
14 to 14.5M ; 43775 ; 5.67% ; 771,553
14.5 to 15M ; 43387 ; 4.80% ; 903,541
15 to 15.5M ; 43695 ; 4.09% ; 1,069,381
15.5M to inf ; 827810 (to 25M); 27.77% ; 2,980,636

Considering that a prime at the current n would be in the top 15 ever found, you should consider 321 while these candidates have such good chances!
____________

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Discovered 4 mega primesEliminated 3 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage321 LLR Sapphire: Earned 20,000,000 credits (34,352,250)Cullen LLR Sapphire: Earned 20,000,000 credits (25,424,693)ESP LLR Sapphire: Earned 20,000,000 credits (22,668,198)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (21,044,302)PPS LLR Emerald: Earned 50,000,000 credits (67,163,078)PSP LLR Sapphire: Earned 20,000,000 credits (23,462,639)SoB LLR Emerald: Earned 50,000,000 credits (58,594,951)SR5 LLR Emerald: Earned 50,000,000 credits (50,308,578)SGS LLR Sapphire: Earned 20,000,000 credits (22,597,792)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Emerald: Earned 50,000,000 credits (51,404,601)Woodall LLR Sapphire: Earned 20,000,000 credits (24,573,411)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (4,024,795)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve Emerald: Earned 50,000,000 credits (50,504,945)PPS Sieve Double Gold: Earned 500,000,000 credits (504,377,255)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,288,222)TRP Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,149,354)AP 26/27 Emerald: Earned 50,000,000 credits (69,229,896)GFN Double Gold: Earned 500,000,000 credits (580,674,019)PSA Double Gold: Earned 500,000,000 credits (530,514,240)
Message 63472 - Posted: 13 Mar 2013 | 14:00:17 UTC

Thanks Roger, this is somehow encouraging :-)
____________
My stats
Badge score: 1*1 + 5*2 + 8*9 + 9*6 + 12*3 = 173

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ID: 16874
Credit: 27,574,825
RAC: 96,053
321 LLR Gold: Earned 500,000 credits (656,177)Cullen LLR Silver: Earned 100,000 credits (457,297)ESP LLR Silver: Earned 100,000 credits (437,502)PPS LLR Amethyst: Earned 1,000,000 credits (1,256,334)SoB LLR Amethyst: Earned 1,000,000 credits (1,246,109)SR5 LLR Ruby: Earned 2,000,000 credits (2,193,129)SGS LLR Silver: Earned 100,000 credits (101,658)Woodall LLR Silver: Earned 100,000 credits (292,129)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (32,498)PPS Sieve Jade: Earned 10,000,000 credits (15,511,858)AP 26/27 Amethyst: Earned 1,000,000 credits (1,491,867)GFN Ruby: Earned 2,000,000 credits (3,796,960)PSA Silver: Earned 100,000 credits (101,309)
Message 63490 - Posted: 14 Mar 2013 | 5:00:40 UTC - in response to Message 63467.

Range ; candidates ; % chance ; 1 in X chance of prime per candidate
9.4 to 9.6M ; 17462 ; 14.98% ; 116,601
9.6 to 9.8M ; 17528 ; 13.68% ; 128,133
9.80 to 10M ; 17402 ; 12.51% ; 139,144
10 to 10.5M ; 43550 ; 26.84% ; 162,287
10.5 to 11M ; 43627 ; 21.62% ; 201,790
11 to 11.5M ; 43365 ; 17.52% ; 247,450
11.5 to 12M ; 43468 ; 14.29% ; 304,089
12 to 12.5M ; 43590 ; 11.73% ; 371,481
12.5 to 13M ; 43264 ; 9.69% ; 446,296
13 to 13.5M ; 43761 ; 8.06% ; 542,982
13.5 to 14M ; 43476 ; 6.74% ; 644,860
14 to 14.5M ; 43775 ; 5.67% ; 771,553
14.5 to 15M ; 43387 ; 4.80% ; 903,541
15 to 15.5M ; 43695 ; 4.09% ; 1,069,381
15.5M to inf ; 827810 (to 25M); 27.77% ; 2,980,636


Am I reading this correct? Are you saying that a candidate in 9.4-9.6 range is 10 times more likely to be a prime than one in the 15-15.5 range? I don't think that is correct.

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Credit: 123,323,373
RAC: 107
321 LLR Amethyst: Earned 1,000,000 credits (1,063,954)Cullen LLR Gold: Earned 500,000 credits (665,748)ESP LLR Amethyst: Earned 1,000,000 credits (1,025,432)Generalized Cullen/Woodall LLR Silver: Earned 100,000 credits (374,632)PPS LLR Turquoise: Earned 5,000,000 credits (5,215,663)PSP LLR Amethyst: Earned 1,000,000 credits (1,134,556)SoB LLR Amethyst: Earned 1,000,000 credits (1,064,898)SR5 LLR Amethyst: Earned 1,000,000 credits (1,043,015)SGS LLR Amethyst: Earned 1,000,000 credits (1,072,821)TRP LLR Amethyst: Earned 1,000,000 credits (1,026,807)Woodall LLR Amethyst: Earned 1,000,000 credits (1,042,977)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,737)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,911,344)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,077,092)PPS Sieve Sapphire: Earned 20,000,000 credits (45,225,274)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,034,014)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,070,774)AP 26/27 Amethyst: Earned 1,000,000 credits (1,913,157)GFN Ruby: Earned 2,000,000 credits (4,084,085)PSA Sapphire: Earned 20,000,000 credits (47,256,391)
Message 63510 - Posted: 15 Mar 2013 | 3:50:54 UTC - in response to Message 63490.

Range ; candidates ; % chance ; 1 in X chance of prime per candidate
9.4 to 9.6M ; 17462 ; 14.98% ; 116,601
9.6 to 9.8M ; 17528 ; 13.68% ; 128,133
9.80 to 10M ; 17402 ; 12.51% ; 139,144
10 to 10.5M ; 43550 ; 26.84% ; 162,287
10.5 to 11M ; 43627 ; 21.62% ; 201,790
11 to 11.5M ; 43365 ; 17.52% ; 247,450
11.5 to 12M ; 43468 ; 14.29% ; 304,089
12 to 12.5M ; 43590 ; 11.73% ; 371,481
12.5 to 13M ; 43264 ; 9.69% ; 446,296
13 to 13.5M ; 43761 ; 8.06% ; 542,982
13.5 to 14M ; 43476 ; 6.74% ; 644,860
14 to 14.5M ; 43775 ; 5.67% ; 771,553
14.5 to 15M ; 43387 ; 4.80% ; 903,541
15 to 15.5M ; 43695 ; 4.09% ; 1,069,381
15.5M to inf ; 827810 (to 25M); 27.77% ; 2,980,636


Am I reading this correct? Are you saying that a candidate in 9.4-9.6 range is 10 times more likely to be a prime than one in the 15-15.5 range? I don't think that is correct.

Intuitively that sounds right to me since as numbers get larger, the probability of a number being prime goes down by quite a bit (i.e.: goes down more than just linearly).
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321 LLR Gold: Earned 500,000 credits (656,177)Cullen LLR Silver: Earned 100,000 credits (457,297)ESP LLR Silver: Earned 100,000 credits (437,502)PPS LLR Amethyst: Earned 1,000,000 credits (1,256,334)SoB LLR Amethyst: Earned 1,000,000 credits (1,246,109)SR5 LLR Ruby: Earned 2,000,000 credits (2,193,129)SGS LLR Silver: Earned 100,000 credits (101,658)Woodall LLR Silver: Earned 100,000 credits (292,129)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (32,498)PPS Sieve Jade: Earned 10,000,000 credits (15,511,858)AP 26/27 Amethyst: Earned 1,000,000 credits (1,491,867)GFN Ruby: Earned 2,000,000 credits (3,796,960)PSA Silver: Earned 100,000 credits (101,309)
Message 63512 - Posted: 15 Mar 2013 | 9:19:44 UTC - in response to Message 63510.

Intuitively that sounds right to me since as numbers get larger, the probability of a number being prime goes down by quite a bit (i.e.: goes down more than just linearly).

Nope. It goes down precisely linearly. This phenomenon is called, surprisingly, "Prime Number Theorem" :)

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Found 1 prime in the 2018 Tour de Primes321 LLR Amethyst: Earned 1,000,000 credits (1,805,841)Cullen LLR Amethyst: Earned 1,000,000 credits (1,305,599)ESP LLR Ruby: Earned 2,000,000 credits (2,085,950)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,050,279)PPS LLR Ruby: Earned 2,000,000 credits (2,149,793)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,493,571)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,072,856)TRP LLR Ruby: Earned 2,000,000 credits (2,066,087)Woodall LLR Amethyst: Earned 1,000,000 credits (1,293,758)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,151)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,422,123)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,227,972)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,021,659)AP 26/27 Sapphire: Earned 20,000,000 credits (20,291,817)GFN Emerald: Earned 50,000,000 credits (55,143,105)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 63557 - Posted: 16 Mar 2013 | 23:44:19 UTC - in response to Message 63512.

Prime Number Theory say that the chance of a random integer x being prime is about 1/log x
http://primes.utm.edu/howmany.shtml#3
For x = 3*2^n+/-1, chance is about 1/log (3*2^n+/-1).
As n gets large this chance approaches 1/n.
____________

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321 LLR Turquoise: Earned 5,000,000 credits (5,007,491)Cullen LLR Ruby: Earned 2,000,000 credits (2,525,919)ESP LLR Turquoise: Earned 5,000,000 credits (5,067,407)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,599,077)PPS LLR Ruby: Earned 2,000,000 credits (2,404,534)PSP LLR Turquoise: Earned 5,000,000 credits (5,037,379)SoB LLR Turquoise: Earned 5,000,000 credits (5,017,796)SR5 LLR Ruby: Earned 2,000,000 credits (2,935,187)SGS LLR Amethyst: Earned 1,000,000 credits (1,074,845)TRP LLR Turquoise: Earned 5,000,000 credits (5,009,956)Woodall LLR Ruby: Earned 2,000,000 credits (2,935,056)321 Sieve (suspended) Bronze: Earned 10,000 credits (32,205)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,323,773)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,011,119)PPS Sieve Emerald: Earned 50,000,000 credits (66,275,679)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,081,558)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,180,919)AP 26/27 Jade: Earned 10,000,000 credits (13,513,022)GFN Double Silver: Earned 200,000,000 credits (301,366,812)
Message 72518 - Posted: 21 Jan 2014 | 7:55:40 UTC
Last modified: 21 Jan 2014 | 8:52:06 UTC

Hello!

Edit :: My bad, it's already reported in this thread:

http://www.primegrid.com/forum_thread.php?id=5462

At least it is now official on the list!

If I'm not wrong, another megaprime is found!
New entry at 12'th place:

http://primes.utm.edu/primes/page.php?id=116922

Seems like 2014 will be a very nice year primewise!!

With regards,

Hans Sveen
Oslo, Norway


Keep on searching!!

What the heck, what is JStriders signature doing here??[/url]
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321 LLR Amethyst: Earned 1,000,000 credits (1,009,885)Cullen LLR Amethyst: Earned 1,000,000 credits (1,440,123)ESP LLR Amethyst: Earned 1,000,000 credits (1,008,511)PPS LLR Ruby: Earned 2,000,000 credits (2,389,215)PSP LLR Amethyst: Earned 1,000,000 credits (1,080,442)SoB LLR Amethyst: Earned 1,000,000 credits (1,143,918)SR5 LLR Amethyst: Earned 1,000,000 credits (1,853,162)SGS LLR Amethyst: Earned 1,000,000 credits (1,344,963)TRP LLR Amethyst: Earned 1,000,000 credits (1,140,037)Woodall LLR Amethyst: Earned 1,000,000 credits (1,130,355)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,038,617)PPS Sieve Sapphire: Earned 20,000,000 credits (36,643,348)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,717)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,298,244)GFN Jade: Earned 10,000,000 credits (17,332,530)PSA Sapphire: Earned 20,000,000 credits (20,125,451)
Message 72522 - Posted: 21 Jan 2014 | 11:02:16 UTC - in response to Message 72518.

Hello1
If I'm not wrong, another megaprime is found!
New entry at 12'th place:

http://primes.utm.edu/primes/page.php?id=116922

Seems like 2014 will be a very nice year primewise!!

With regards,

Hans Sveen
Oslo, Norway


Keep on searching!!

What the heck, what is JStriders signature doing here??!


Yep, that's one of the mega primes mentioned in this thread[/]. As is also posted there I believe, there hasn't been an official announcement here because there are still some tests being run :)

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321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 72547 - Posted: 22 Jan 2014 | 16:55:03 UTC

The last "-" 321 prime is: 3*2^6090515-1 1833429 L1353 2010. Will the 2n rule be broken? I.e. to date there has always been at least on prime less than exponent 2n where there has been a prime for exponent n. So, given PG is crunching at 10862313, PG should find a "-" 321 prime real soon, fingers crossed, toes crossed, rabbit's foot worn,... :-)

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Message 79638 - Posted: 21 Sep 2014 | 18:08:55 UTC - in response to Message 72547.

I am crunching 321 on an old (4 core) Q6600 now, with a reasonable chance of finding a huge prime. Tests are taking 60 hours per core -- that is about 11 tests per week for the box. I pleased to say that PG on BOINC works seamlessly.

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Message 80008 - Posted: 5 Oct 2014 | 13:53:12 UTC - in response to Message 79638.

Last night, my old Q6600 blew up with a bang! followed by a great stink. I stripped down the box and in the process broke the mounting bracket for the Arctic Freezer 7. I now have some spare parts! I put my old faithful Tyan 4x4 AMD CPU onto 321. I will get about 30-35 tests per week out of it.

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Found 2 primes in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,008,573)Cullen LLR Turquoise: Earned 5,000,000 credits (5,005,909)ESP LLR Turquoise: Earned 5,000,000 credits (5,003,216)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,004,937)PPS LLR Ruby: Earned 2,000,000 credits (3,287,539)PSP LLR Ruby: Earned 2,000,000 credits (3,998,562)SoB LLR Turquoise: Earned 5,000,000 credits (8,031,952)SR5 LLR Ruby: Earned 2,000,000 credits (3,004,172)SGS LLR Ruby: Earned 2,000,000 credits (2,555,530)TRP LLR Ruby: Earned 2,000,000 credits (3,000,132)Woodall LLR Ruby: Earned 2,000,000 credits (2,988,875)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (268,250)Generalized Cullen/Woodall Sieve Jade: Earned 10,000,000 credits (10,000,502)PPS Sieve Double Silver: Earned 200,000,000 credits (266,666,326)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,000,133)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,000,970)AP 26/27 Emerald: Earned 50,000,000 credits (94,998,371)GFN Emerald: Earned 50,000,000 credits (93,186,999)PSA Emerald: Earned 50,000,000 credits (90,000,001)
Message 80009 - Posted: 5 Oct 2014 | 14:20:44 UTC

Once I've topped out the final few SGS, helped a bit with TRP clean-up & got my final 10 WOO in the bag, I'll be joining you for 1000000cr/(25k/dy)=40 days.

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321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 80273 - Posted: 13 Oct 2014 | 20:04:44 UTC

Well I have been running the quad socket Tyan for 10 days and have these stats:

State: All 49 | In progress 16 | Pending 1 | Inconclusive 13 | Valid 7 | Aborted | Invalid 12 | Error

I think I have fixed the issues with it. Mostly turning "throttle" "enabled" -- for some reason the BIOS had reset itself after a long period of no use; and active cooling of the HT heatspeaders.

There is some consolation: I have my 321 gold badge!

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Found 2 primes in the 2018 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,008,573)Cullen LLR Turquoise: Earned 5,000,000 credits (5,005,909)ESP LLR Turquoise: Earned 5,000,000 credits (5,003,216)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (5,004,937)PPS LLR Ruby: Earned 2,000,000 credits (3,287,539)PSP LLR Ruby: Earned 2,000,000 credits (3,998,562)SoB LLR Turquoise: Earned 5,000,000 credits (8,031,952)SR5 LLR Ruby: Earned 2,000,000 credits (3,004,172)SGS LLR Ruby: Earned 2,000,000 credits (2,555,530)TRP LLR Ruby: Earned 2,000,000 credits (3,000,132)Woodall LLR Ruby: Earned 2,000,000 credits (2,988,875)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (268,250)Generalized Cullen/Woodall Sieve Jade: Earned 10,000,000 credits (10,000,502)PPS Sieve Double Silver: Earned 200,000,000 credits (266,666,326)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,000,133)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,000,970)AP 26/27 Emerald: Earned 50,000,000 credits (94,998,371)GFN Emerald: Earned 50,000,000 credits (93,186,999)PSA Emerald: Earned 50,000,000 credits (90,000,001)
Message 80277 - Posted: 13 Oct 2014 | 20:52:32 UTC

Well done :).

After the BIOS reset, did you load optimised defaults or a similar option?

Paul Underwood
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321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 80278 - Posted: 13 Oct 2014 | 21:30:12 UTC - in response to Message 80277.
Last modified: 13 Oct 2014 | 21:34:58 UTC

Well done :).

After the BIOS reset, did you load optimised defaults or a similar option?


No. I just poked around. The OS was to windows -- I am Linux. I had to tweak which graphics card to use. Turned off floppy. Made IMMOU 1GB. Turn on throttle. Turn on PowerNow. And a few other non performance related things.

I really hope it is 100% for 321 now. I will give another week and if there is no improvement I will have to think again.

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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,063,182)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (2,001,789)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,004,898)PPS LLR Ruby: Earned 2,000,000 credits (2,082,200)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (24,608,301)SR5 LLR Turquoise: Earned 5,000,000 credits (7,371,106)SGS LLR Ruby: Earned 2,000,000 credits (2,010,466)TRP LLR Ruby: Earned 2,000,000 credits (2,433,520)Woodall LLR Ruby: Earned 2,000,000 credits (2,121,460)321 Sieve (suspended) Silver: Earned 100,000 credits (200,576)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (3,708,149)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Turquoise: Earned 5,000,000 credits (7,086,053)GFN Emerald: Earned 50,000,000 credits (53,445,753)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 80282 - Posted: 14 Oct 2014 | 5:11:15 UTC - in response to Message 80278.

Typically that problem is caused by overclocking.
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Message 80294 - Posted: 14 Oct 2014 | 12:16:07 UTC - in response to Message 80282.

Typically that problem is caused by overclocking.



The Tyan has no overclocking. I think my problem was the throttle and hot HTs. I should get the first results through with the new settings in a couple of days

I hope others will not overclock! A 5% speed up is not worth it if 1 in 10 results are bad.

Paul Underwood
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Message 80332 - Posted: 16 Oct 2014 | 15:02:23 UTC

As far as I can tell, 4 day 321 tests seems to continue to turn in invalid results on the Tyan. I have moved it over to SGS and will see how it gets on there.

Profile Michael GoetzProject donor
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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,063,182)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (2,001,789)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,004,898)PPS LLR Ruby: Earned 2,000,000 credits (2,082,200)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (24,608,301)SR5 LLR Turquoise: Earned 5,000,000 credits (7,371,106)SGS LLR Ruby: Earned 2,000,000 credits (2,010,466)TRP LLR Ruby: Earned 2,000,000 credits (2,433,520)Woodall LLR Ruby: Earned 2,000,000 credits (2,121,460)321 Sieve (suspended) Silver: Earned 100,000 credits (200,576)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (3,708,149)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Turquoise: Earned 5,000,000 credits (7,086,053)GFN Emerald: Earned 50,000,000 credits (53,445,753)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 80333 - Posted: 16 Oct 2014 | 15:17:44 UTC - in response to Message 80332.

As far as I can tell, 4 day 321 tests seems to continue to turn in invalid results on the Tyan. I have moved it over to SGS and will see how it gets on there.


You'll see a higher percentage of successful tasks, but that's only because the much shorter tasks are more likely to finish before an error occurs. The problem won't go away. If anything, shorter tasks are actually tougher on the CPU because of the smaller FFT sizes.

If you're not overclocking, the next most common problem is bad memory. Sometimes this can be corrected by removing and reseating the memory cards.

Next after that is overheating. If the heatsinks and fans are clogged with dust, or coated with smoke residue from either cooking or tobacco, the CPU or motherboard components could be overheating and malfunctioning.

Also try disabling anti-virus programs, or excluding them from the BOINC directories. (Note: with AVG you need to completely disable it's "identity protection" system. It can't be excluded from individual directories and it DOES cause problems with BOINC.)

I've never heard of a throttling problem causing errors, but I suppose anything is possible.
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Message 80932 - Posted: 24 Nov 2014 | 11:58:02 UTC

1 0.0000000 2 2.0000000 3 1.5000000 4 1.3333333 6 1.5000000 7 1.1666667 11 1.5714286 18 1.6363636 34 1.8888889 38 1.1176471 43 1.1315789 55 1.2790698 64 1.1636364 76 1.1875000 94 1.2368421 103 1.0957447 143 1.3883495 206 1.4405594 216 1.0485437 306 1.4166667 324 1.0588235 391 1.2067901 458 1.1713555 470 1.0262009 827 1.7595745 1274 1.5405079 3276 2.5714286 4204 1.2832723 5134 1.2212179 7559 1.4723413 12676 1.6769414 14898 1.1752919 18123 1.2164720 18819 1.0384042 25690 1.3651097 26459 1.0299338 41628 1.5733021 51387 1.2344336 71783 1.3969097 80330 1.1190672 85687 1.0666874 88171 1.0289892 97063 1.1008495 123630 1.2737088 155930 1.2612634 164987 1.0580838 234760 1.4229000 414840 1.7670813 584995 1.4101702 702038 1.2000752 727699 1.0365522 992700 1.3641629 1201046 1.2098781 1232255 1.0259848 2312734 1.8768307 3136255 1.3560812 4235414 1.3504686 6090515 1.4379976 11484018 1.8855578


The average increase, over the previous, is 1.3512676. So it seems to me the next 321 (minus form) will come very soon.
[/code]

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Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,614,439)Cullen LLR Ruby: Earned 2,000,000 credits (2,440,687)ESP LLR Turquoise: Earned 5,000,000 credits (5,019,435)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,029,174)PPS LLR Turquoise: Earned 5,000,000 credits (5,800,071)PSP LLR Turquoise: Earned 5,000,000 credits (5,000,433)SoB LLR Ruby: Earned 2,000,000 credits (4,087,062)SR5 LLR Turquoise: Earned 5,000,000 credits (5,040,727)SGS LLR Ruby: Earned 2,000,000 credits (3,142,971)TRP LLR Jade: Earned 10,000,000 credits (11,796,391)Woodall LLR Ruby: Earned 2,000,000 credits (2,282,622)321 Sieve (suspended) Silver: Earned 100,000 credits (200,818)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (59,788,598)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,056,778)PPS Sieve Double Silver: Earned 200,000,000 credits (450,508,567)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Jade: Earned 10,000,000 credits (10,130,821)TRP Sieve (suspended) Jade: Earned 10,000,000 credits (10,074,710)AP 26/27 Gold: Earned 500,000 credits (530,229)GFN Double Bronze: Earned 100,000,000 credits (106,896,662)PSA Emerald: Earned 50,000,000 credits (62,378,755)
Message 80941 - Posted: 24 Nov 2014 | 20:25:47 UTC

What I'd like to see would be a 3*2^n +/- 1 twin prime in the range we're searching now. Wouldn't that be an event! I know, I know, "don't hold your breath". :-)

--Gary

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321 LLR Bronze: Earned 10,000 credits (48,835)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Bronze: Earned 10,000 credits (13,226)PPS LLR Amethyst: Earned 1,000,000 credits (1,620,904)SoB LLR Silver: Earned 100,000 credits (132,293)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (14,746)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 83136 - Posted: 1 Feb 2015 | 14:47:20 UTC - in response to Message 80941.

What I'd like to see would be a 3*2^n +/- 1 twin prime in the range we're searching now. Wouldn't that be an event! I know, I know, "don't hold your breath". :-)

--Gary


Also see OEIS A181490. /JeppeSN

Paul Underwood
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Posts: 66
ID: 25545
Credit: 3,482,191
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321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 84177 - Posted: 19 Mar 2015 | 3:11:30 UTC

1 0.0000000 2 2.0000000 3 1.5000000 4 1.3333333 6 1.5000000 7 1.1666667 11 1.5714286 18 1.6363636 34 1.8888889 38 1.1176471 43 1.1315789 55 1.2790698 64 1.1636364 76 1.1875000 94 1.2368421 103 1.0957447 143 1.3883495 206 1.4405594 216 1.0485437 306 1.4166667 324 1.0588235 391 1.2067901 458 1.1713555 470 1.0262009 827 1.7595745 1274 1.5405079 3276 2.5714286 4204 1.2832723 5134 1.2212179 7559 1.4723413 12676 1.6769414 14898 1.1752919 18123 1.2164720 18819 1.0384042 25690 1.3651097 26459 1.0299338 41628 1.5733021 51387 1.2344336 71783 1.3969097 80330 1.1190672 85687 1.0666874 88171 1.0289892 97063 1.1008495 123630 1.2737088 155930 1.2612634 164987 1.0580838 234760 1.4229000 414840 1.7670813 584995 1.4101702 702038 1.2000752 727699 1.0365522 992700 1.3641629 1201046 1.2098781 1232255 1.0259848 2312734 1.8768307 3136255 1.3560812 4235414 1.3504686 6090515 1.4379976 11484018 1.8855578 11731850 1.0215806


The average increase is now 1.3456797, so just maybe we will not have to wait very long for the next 321 (minus form) prime. Of course, in the mean time a plus form might be found ;-)

Paul Underwood
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321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 86430 - Posted: 26 Jun 2015 | 20:57:23 UTC

1 0.0000000 2 2.0000000 3 1.5000000 4 1.3333333 6 1.5000000 7 1.1666667 11 1.5714286 18 1.6363636 34 1.8888889 38 1.1176471 43 1.1315789 55 1.2790698 64 1.1636364 76 1.1875000 94 1.2368421 103 1.0957447 143 1.3883495 206 1.4405594 216 1.0485437 306 1.4166667 324 1.0588235 391 1.2067901 458 1.1713555 470 1.0262009 827 1.7595745 1274 1.5405079 3276 2.5714286 4204 1.2832723 5134 1.2212179 7559 1.4723413 12676 1.6769414 14898 1.1752919 18123 1.2164720 18819 1.0384042 25690 1.3651097 26459 1.0299338 41628 1.5733021 51387 1.2344336 71783 1.3969097 80330 1.1190672 85687 1.0666874 88171 1.0289892 97063 1.1008495 123630 1.2737088 155930 1.2612634 164987 1.0580838 234760 1.4229000 414840 1.7670813 584995 1.4101702 702038 1.2000752 727699 1.0365522 992700 1.3641629 1201046 1.2098781 1232255 1.0259848 2312734 1.8768307 3136255 1.3560812 4235414 1.3504686 6090515 1.4379976 11484018 1.8855578 11731850 1.0215806 11895718 1.0139678


The average is now 1.3401511. Can we expect a fourth bus to come along? ;-)

Paul Underwood
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321 LLR Ruby: Earned 2,000,000 credits (3,455,288)PSA Bronze: Earned 10,000 credits (22,365)
Message 116149 - Posted: 19 Mar 2018 | 8:21:27 UTC - in response to Message 86430.

-99.70% 1.22428235452968 14059680.5965012 -95.00% 1.26290528305169 14503227.0028607 -68.00% 1.30152821157371 14946773.4092203 average 1.3401511 15390319.8155799 68.00% 1.37877406861775 15833866.2219395 95.00% 1.41739699713977 16277412.628299 99.70% 1.45601992566179 16720959.0346586


Is my calculation for next 3*2^n-1 prime.

Today the Year of the Dog challenge passed the 14M bit mark.

There is also a 3*2^n+1 prime out there somewhere.

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321 LLR Sapphire: Earned 20,000,000 credits (20,060,555)Cullen LLR Gold: Earned 500,000 credits (533,200)ESP LLR Silver: Earned 100,000 credits (314,648)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (67,663)PPS LLR Gold: Earned 500,000 credits (897,985)PSP LLR Gold: Earned 500,000 credits (719,124)SoB LLR Silver: Earned 100,000 credits (485,642)SR5 LLR Amethyst: Earned 1,000,000 credits (1,003,678)SGS LLR Silver: Earned 100,000 credits (128,562)TRP LLR Silver: Earned 100,000 credits (297,460)Woodall LLR Silver: Earned 100,000 credits (380,849)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,064,320)PPS Sieve Emerald: Earned 50,000,000 credits (61,439,846)AP 26/27 Amethyst: Earned 1,000,000 credits (1,524,211)GFN Sapphire: Earned 20,000,000 credits (32,373,747)PSA Emerald: Earned 50,000,000 credits (72,546,119)
Message 120017 - Posted: 17 Aug 2018 | 7:59:06 UTC

I did a fun calculation based on the density distribution of the ratios and their local peaks using a kernel density estimation.

Basically I just look at around which ratios "clump" together and assume that there would be some systematic behaviour in it (which there most likely is not). The statistics are also quite low. I excluded a few of the first ratios.

I predict that 321*n-1 will be prime at

ratio, chance, n
1.34 41.46 % 15940262
1.566 15.65 % 18628694
1.65 9.79 % 19627935
1.762 11.20 % 20960255
1.886 16.37 % 22435324
2.571 5.53 % 30583891

There is also a local "clumps" at 1.042 and 1.209, but we are already past these.

I predict that 321*n+1 will be prime at

ratio, chance, n
1.342 25.82 % 14532982
1.541 9.33 % 16688022
1.626 14.71 % 17608517
1.854 9.10 % 20077607
1.987 13.63 % 21517911
2.864 9.14 % 31015247
4.135 9.14 % 44779346
5.345 9.14 % 57882854

There is also a local "clumps" at 1.067, 1.139 and 1.22, but we are already past these.

These numbers are based on the local peaks of the distribution, so the error estimates are very large!

But I would say that there is a possibility that a 321*n+1 prime is close :)

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321 LLR Bronze: Earned 10,000 credits (48,835)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Bronze: Earned 10,000 credits (13,226)PPS LLR Amethyst: Earned 1,000,000 credits (1,620,904)SoB LLR Silver: Earned 100,000 credits (132,293)SR5 LLR Bronze: Earned 10,000 credits (16,010)TRP LLR Bronze: Earned 10,000 credits (14,746)Woodall LLR Silver: Earned 100,000 credits (109,455)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 120033 - Posted: 17 Aug 2018 | 20:51:51 UTC - in response to Message 120017.

Do you write 321*n±1 to mean 3*2^n±1?

They are not the same. While 321*n±1 is known to be prime infinitely often (each arithmetic progression a*n+1 or a*n-1 contains infinitely many primes), for almost all really big values of n there is no efficient way to check if 321*n±1 is prime.

The numbers 3*2^n±1 are much more scarce, but for each of them there is an efficient way to check its primality.

/JeppeSN

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321 LLR Sapphire: Earned 20,000,000 credits (20,060,555)Cullen LLR Gold: Earned 500,000 credits (533,200)ESP LLR Silver: Earned 100,000 credits (314,648)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (67,663)PPS LLR Gold: Earned 500,000 credits (897,985)PSP LLR Gold: Earned 500,000 credits (719,124)SoB LLR Silver: Earned 100,000 credits (485,642)SR5 LLR Amethyst: Earned 1,000,000 credits (1,003,678)SGS LLR Silver: Earned 100,000 credits (128,562)TRP LLR Silver: Earned 100,000 credits (297,460)Woodall LLR Silver: Earned 100,000 credits (380,849)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,064,320)PPS Sieve Emerald: Earned 50,000,000 credits (61,439,846)AP 26/27 Amethyst: Earned 1,000,000 credits (1,524,211)GFN Sapphire: Earned 20,000,000 credits (32,373,747)PSA Emerald: Earned 50,000,000 credits (72,546,119)
Message 120034 - Posted: 18 Aug 2018 | 9:44:44 UTC - in response to Message 120033.

Ugh! :D

I definately mean 3*2^n-1 and 3*2^n+1!

Just a brain fart on my part :)

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321 LLR Sapphire: Earned 20,000,000 credits (20,060,555)Cullen LLR Gold: Earned 500,000 credits (533,200)ESP LLR Silver: Earned 100,000 credits (314,648)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (67,663)PPS LLR Gold: Earned 500,000 credits (897,985)PSP LLR Gold: Earned 500,000 credits (719,124)SoB LLR Silver: Earned 100,000 credits (485,642)SR5 LLR Amethyst: Earned 1,000,000 credits (1,003,678)SGS LLR Silver: Earned 100,000 credits (128,562)TRP LLR Silver: Earned 100,000 credits (297,460)Woodall LLR Silver: Earned 100,000 credits (380,849)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,064,320)PPS Sieve Emerald: Earned 50,000,000 credits (61,439,846)AP 26/27 Amethyst: Earned 1,000,000 credits (1,524,211)GFN Sapphire: Earned 20,000,000 credits (32,373,747)PSA Emerald: Earned 50,000,000 credits (72,546,119)
Message 120051 - Posted: 20 Aug 2018 | 8:14:43 UTC

Also: based on my tests, the FFT size will increase from 768K to 800K at n=14536766.

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321 LLR Sapphire: Earned 20,000,000 credits (20,060,555)Cullen LLR Gold: Earned 500,000 credits (533,200)ESP LLR Silver: Earned 100,000 credits (314,648)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (67,663)PPS LLR Gold: Earned 500,000 credits (897,985)PSP LLR Gold: Earned 500,000 credits (719,124)SoB LLR Silver: Earned 100,000 credits (485,642)SR5 LLR Amethyst: Earned 1,000,000 credits (1,003,678)SGS LLR Silver: Earned 100,000 credits (128,562)TRP LLR Silver: Earned 100,000 credits (297,460)Woodall LLR Silver: Earned 100,000 credits (380,849)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,064,320)PPS Sieve Emerald: Earned 50,000,000 credits (61,439,846)AP 26/27 Amethyst: Earned 1,000,000 credits (1,524,211)GFN Sapphire: Earned 20,000,000 credits (32,373,747)PSA Emerald: Earned 50,000,000 credits (72,546,119)
Message 121015 - Posted: 11 Oct 2018 | 6:39:54 UTC - in response to Message 120051.

Also: based on my tests, the FFT size will increase from 768K to 800K at n=14536766.


By my calculations, there is about 1100-1200 candidates left before the rise in FFT size, which is about a 4.2% increase.

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321 LLR Bronze: Earned 10,000 credits (32,089)ESP LLR Silver: Earned 100,000 credits (102,363)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (16,261)PPS LLR Silver: Earned 100,000 credits (135,849)PSP LLR Bronze: Earned 10,000 credits (47,200)SoB LLR Gold: Earned 500,000 credits (696,995)SR5 LLR Bronze: Earned 10,000 credits (15,939)SGS LLR Bronze: Earned 10,000 credits (11,814)TRP LLR Bronze: Earned 10,000 credits (40,836)Woodall LLR Bronze: Earned 10,000 credits (36,435)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,682,471)PPS Sieve Bronze: Earned 10,000 credits (13,484)AP 26/27 Bronze: Earned 10,000 credits (56,602)GFN Silver: Earned 100,000 credits (140,432)PSA Silver: Earned 100,000 credits (232,200)
Message 123029 - Posted: 30 Nov 2018 | 10:06:56 UTC - in response to Message 121015.

Also: based on my tests, the FFT size will increase from 768K to 800K at n=14536766.


By my calculations, there is about 1100-1200 candidates left before the rise in FFT size, which is about a 4.2% increase.


Can you say when the next FFT increase occures?

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321 LLR Sapphire: Earned 20,000,000 credits (20,060,555)Cullen LLR Gold: Earned 500,000 credits (533,200)ESP LLR Silver: Earned 100,000 credits (314,648)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (67,663)PPS LLR Gold: Earned 500,000 credits (897,985)PSP LLR Gold: Earned 500,000 credits (719,124)SoB LLR Silver: Earned 100,000 credits (485,642)SR5 LLR Amethyst: Earned 1,000,000 credits (1,003,678)SGS LLR Silver: Earned 100,000 credits (128,562)TRP LLR Silver: Earned 100,000 credits (297,460)Woodall LLR Silver: Earned 100,000 credits (380,849)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,064,320)PPS Sieve Emerald: Earned 50,000,000 credits (61,439,846)AP 26/27 Amethyst: Earned 1,000,000 credits (1,524,211)GFN Sapphire: Earned 20,000,000 credits (32,373,747)PSA Emerald: Earned 50,000,000 credits (72,546,119)
Message 123137 - Posted: 4 Dec 2018 | 19:06:59 UTC - in response to Message 123029.

Also: based on my tests, the FFT size will increase from 768K to 800K at n=14536766.


By my calculations, there is about 1100-1200 candidates left before the rise in FFT size, which is about a 4.2% increase.


Can you say when the next FFT increase occures?


Testing with LLR app, the next FFT size increase is at n=15120798, from 800K to 864K. Dunno if there are other machine-specific variables affecting when the FFT sizes increase.

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The "Shut up already!" badge:  This loud mouth has mansplained on the forums over 10 thousand times!  Sheesh!!!Discovered the World's First GFN-19 prime!!!Discovered 1 mega primeFound 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,063,182)Cullen LLR Ruby: Earned 2,000,000 credits (2,005,249)ESP LLR Ruby: Earned 2,000,000 credits (2,001,789)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,004,898)PPS LLR Ruby: Earned 2,000,000 credits (2,082,200)PSP LLR Ruby: Earned 2,000,000 credits (2,632,269)SoB LLR Sapphire: Earned 20,000,000 credits (24,608,301)SR5 LLR Turquoise: Earned 5,000,000 credits (7,371,106)SGS LLR Ruby: Earned 2,000,000 credits (2,010,466)TRP LLR Ruby: Earned 2,000,000 credits (2,433,520)Woodall LLR Ruby: Earned 2,000,000 credits (2,121,460)321 Sieve (suspended) Silver: Earned 100,000 credits (200,576)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,170,256)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (3,708,149)PPS Sieve Sapphire: Earned 20,000,000 credits (20,110,788)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,035,522)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,051,121)AP 26/27 Turquoise: Earned 5,000,000 credits (7,086,053)GFN Emerald: Earned 50,000,000 credits (53,445,753)PSA Jade: Earned 10,000,000 credits (10,038,118)
Message 123141 - Posted: 4 Dec 2018 | 20:01:51 UTC - in response to Message 123137.

Testing with LLR app, the next FFT size increase is at n=15120798, from 800K to 864K. Dunno if there are other machine-specific variables affecting when the FFT sizes increase.


+1 and -1 will have FFT transitions at different points.

I think most or all Intel FMA3 CPUs (Haswell+) will transition at the same point.
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