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Message boards : 321 Prime Search : Next Prime

Author Message
Paul Underwood
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Joined: 14 Jul 08
Posts: 56
ID: 25545
Credit: 3,455,122
RAC: 4,524
321 LLR Ruby: Earned 2,000,000 credits (3,428,218)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: 56
ID: 25545
Credit: 3,455,122
RAC: 4,524
321 LLR Ruby: Earned 2,000,000 credits (3,428,218)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,

Profile Roger
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Joined: 27 Nov 11
Posts: 925
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Credit: 181,731,069
RAC: 219,106
321 LLR Amethyst: Earned 1,000,000 credits (1,130,571)Cullen LLR Amethyst: Earned 1,000,000 credits (1,040,598)ESP LLR Amethyst: Earned 1,000,000 credits (1,019,489)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,088,286)PPS LLR Amethyst: Earned 1,000,000 credits (1,002,303)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,071,208)SR5 LLR Ruby: Earned 2,000,000 credits (2,035,801)SGS LLR Amethyst: Earned 1,000,000 credits (1,444,736)TRP LLR Amethyst: Earned 1,000,000 credits (1,352,100)Woodall LLR Amethyst: Earned 1,000,000 credits (1,059,108)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,025,618)PPS Sieve Emerald: Earned 50,000,000 credits (50,443,677)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 Jade: Earned 10,000,000 credits (10,204,532)GFN Emerald: Earned 50,000,000 credits (52,654,727)PSA Sapphire: Earned 20,000,000 credits (43,287,527)
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%
____________

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Joined: 27 Nov 11
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321 LLR Amethyst: Earned 1,000,000 credits (1,130,571)Cullen LLR Amethyst: Earned 1,000,000 credits (1,040,598)ESP LLR Amethyst: Earned 1,000,000 credits (1,019,489)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,088,286)PPS LLR Amethyst: Earned 1,000,000 credits (1,002,303)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,071,208)SR5 LLR Ruby: Earned 2,000,000 credits (2,035,801)SGS LLR Amethyst: Earned 1,000,000 credits (1,444,736)TRP LLR Amethyst: Earned 1,000,000 credits (1,352,100)Woodall LLR Amethyst: Earned 1,000,000 credits (1,059,108)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,025,618)PPS Sieve Emerald: Earned 50,000,000 credits (50,443,677)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 Jade: Earned 10,000,000 credits (10,204,532)GFN Emerald: Earned 50,000,000 credits (52,654,727)PSA Sapphire: Earned 20,000,000 credits (43,287,527)
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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Joined: 15 Aug 05
Posts: 1605
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Credit: 1,751,168,431
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321 LLR Jade: Earned 10,000,000 credits (14,782,476)Cullen LLR Sapphire: Earned 20,000,000 credits (20,758,697)ESP LLR Sapphire: Earned 20,000,000 credits (20,183,757)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (21,044,302)PPS LLR Emerald: Earned 50,000,000 credits (51,016,093)PSP LLR Sapphire: Earned 20,000,000 credits (23,462,639)SoB LLR Sapphire: Earned 20,000,000 credits (22,553,364)SR5 LLR Sapphire: Earned 20,000,000 credits (20,233,642)SGS LLR Sapphire: Earned 20,000,000 credits (20,037,618)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Jade: Earned 10,000,000 credits (18,588,622)Woodall LLR Sapphire: Earned 20,000,000 credits (20,037,694)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 Sapphire: Earned 20,000,000 credits (20,357,260)PPS Sieve Double Silver: Earned 200,000,000 credits (373,417,276)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 Sapphire: Earned 20,000,000 credits (20,062,973)GFN Double Gold: Earned 500,000,000 credits (510,952,939)PSA Double Gold: Earned 500,000,000 credits (525,027,972)
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 + 7*2 + 8*12 + 9*1 + 11*1 + 12*2 = 165

Paul Underwood
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Joined: 14 Jul 08
Posts: 56
ID: 25545
Credit: 3,455,122
RAC: 4,524
321 LLR Ruby: Earned 2,000,000 credits (3,428,218)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: 925
ID: 120786
Credit: 181,731,069
RAC: 219,106
321 LLR Amethyst: Earned 1,000,000 credits (1,130,571)Cullen LLR Amethyst: Earned 1,000,000 credits (1,040,598)ESP LLR Amethyst: Earned 1,000,000 credits (1,019,489)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,088,286)PPS LLR Amethyst: Earned 1,000,000 credits (1,002,303)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,071,208)SR5 LLR Ruby: Earned 2,000,000 credits (2,035,801)SGS LLR Amethyst: Earned 1,000,000 credits (1,444,736)TRP LLR Amethyst: Earned 1,000,000 credits (1,352,100)Woodall LLR Amethyst: Earned 1,000,000 credits (1,059,108)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,025,618)PPS Sieve Emerald: Earned 50,000,000 credits (50,443,677)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 Jade: Earned 10,000,000 credits (10,204,532)GFN Emerald: Earned 50,000,000 credits (52,654,727)PSA Sapphire: Earned 20,000,000 credits (43,287,527)
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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Credit: 181,731,069
RAC: 219,106
321 LLR Amethyst: Earned 1,000,000 credits (1,130,571)Cullen LLR Amethyst: Earned 1,000,000 credits (1,040,598)ESP LLR Amethyst: Earned 1,000,000 credits (1,019,489)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,088,286)PPS LLR Amethyst: Earned 1,000,000 credits (1,002,303)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,071,208)SR5 LLR Ruby: Earned 2,000,000 credits (2,035,801)SGS LLR Amethyst: Earned 1,000,000 credits (1,444,736)TRP LLR Amethyst: Earned 1,000,000 credits (1,352,100)Woodall LLR Amethyst: Earned 1,000,000 credits (1,059,108)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,025,618)PPS Sieve Emerald: Earned 50,000,000 credits (50,443,677)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 Jade: Earned 10,000,000 credits (10,204,532)GFN Emerald: Earned 50,000,000 credits (52,654,727)PSA Sapphire: Earned 20,000,000 credits (43,287,527)
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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Posts: 1605
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321 LLR Jade: Earned 10,000,000 credits (14,782,476)Cullen LLR Sapphire: Earned 20,000,000 credits (20,758,697)ESP LLR Sapphire: Earned 20,000,000 credits (20,183,757)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (21,044,302)PPS LLR Emerald: Earned 50,000,000 credits (51,016,093)PSP LLR Sapphire: Earned 20,000,000 credits (23,462,639)SoB LLR Sapphire: Earned 20,000,000 credits (22,553,364)SR5 LLR Sapphire: Earned 20,000,000 credits (20,233,642)SGS LLR Sapphire: Earned 20,000,000 credits (20,037,618)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Jade: Earned 10,000,000 credits (18,588,622)Woodall LLR Sapphire: Earned 20,000,000 credits (20,037,694)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 Sapphire: Earned 20,000,000 credits (20,357,260)PPS Sieve Double Silver: Earned 200,000,000 credits (373,417,276)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 Sapphire: Earned 20,000,000 credits (20,062,973)GFN Double Gold: Earned 500,000,000 credits (510,952,939)PSA Double Gold: Earned 500,000,000 credits (525,027,972)
Message 63472 - Posted: 13 Mar 2013 | 14:00:17 UTC

Thanks Roger, this is somehow encouraging :-)
____________
My stats
Badge score: 1*1 + 5*2 + 7*2 + 8*12 + 9*1 + 11*1 + 12*2 = 165

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321 LLR Silver: Earned 100,000 credits (115,840)Cullen LLR Silver: Earned 100,000 credits (175,895)ESP LLR Silver: Earned 100,000 credits (330,310)PPS LLR Gold: Earned 500,000 credits (748,824)SoB LLR Silver: Earned 100,000 credits (176,825)SR5 LLR Ruby: Earned 2,000,000 credits (2,010,622)SGS LLR Silver: Earned 100,000 credits (101,658)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (32,498)PPS Sieve Ruby: Earned 2,000,000 credits (2,479,572)GFN Ruby: Earned 2,000,000 credits (2,380,031)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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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 (120,091)PPS LLR Turquoise: Earned 5,000,000 credits (5,123,986)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 (1,005,623)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 Amethyst: Earned 1,000,000 credits (1,782,743)PPS Sieve Sapphire: Earned 20,000,000 credits (45,157,854)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 (1,169,245)GFN Ruby: Earned 2,000,000 credits (3,800,771)PSA Sapphire: Earned 20,000,000 credits (46,607,721)
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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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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321 LLR Amethyst: Earned 1,000,000 credits (1,130,571)Cullen LLR Amethyst: Earned 1,000,000 credits (1,040,598)ESP LLR Amethyst: Earned 1,000,000 credits (1,019,489)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,088,286)PPS LLR Amethyst: Earned 1,000,000 credits (1,002,303)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,071,208)SR5 LLR Ruby: Earned 2,000,000 credits (2,035,801)SGS LLR Amethyst: Earned 1,000,000 credits (1,444,736)TRP LLR Amethyst: Earned 1,000,000 credits (1,352,100)Woodall LLR Amethyst: Earned 1,000,000 credits (1,059,108)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,025,618)PPS Sieve Emerald: Earned 50,000,000 credits (50,443,677)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 Jade: Earned 10,000,000 credits (10,204,532)GFN Emerald: Earned 50,000,000 credits (52,654,727)PSA Sapphire: Earned 20,000,000 credits (43,287,527)
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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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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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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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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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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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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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?

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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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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.

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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.

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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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Credit: 736,925,880
RAC: 27,152
321 LLR Ruby: Earned 2,000,000 credits (2,267,162)Cullen LLR Ruby: Earned 2,000,000 credits (2,277,342)ESP LLR Ruby: Earned 2,000,000 credits (3,085,940)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (785,907)PPS LLR Turquoise: Earned 5,000,000 credits (5,313,186)PSP LLR Ruby: Earned 2,000,000 credits (4,147,471)SoB LLR Ruby: Earned 2,000,000 credits (2,194,447)SR5 LLR Ruby: Earned 2,000,000 credits (3,573,827)SGS LLR Ruby: Earned 2,000,000 credits (2,556,840)TRP LLR Jade: Earned 10,000,000 credits (10,019,191)Woodall LLR Ruby: Earned 2,000,000 credits (2,100,141)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 (446,904,968)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 Silver: Earned 100,000 credits (227,004)GFN Double Bronze: Earned 100,000,000 credits (106,842,054)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

JeppeSNProject donor
Send message
Joined: 5 Apr 14
Posts: 550
ID: 306875
Credit: 7,560,812
RAC: 8,914
PSA Turquoise: Earned 5,000,000 credits (7,560,812)
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
Send message
Joined: 14 Jul 08
Posts: 56
ID: 25545
Credit: 3,455,122
RAC: 4,524
321 LLR Ruby: Earned 2,000,000 credits (3,428,218)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
Send message
Joined: 14 Jul 08
Posts: 56
ID: 25545
Credit: 3,455,122
RAC: 4,524
321 LLR Ruby: Earned 2,000,000 credits (3,428,218)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? ;-)

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