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Message boards : The Riesel Problem : Chance of TRP Prime

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Profile Roger
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Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,530,863
RAC: 1,408
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,213,934)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)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 (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,515,310)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 65923 - Posted: 26 May 2013 | 13:47:54 UTC

For all the remaining TRP k's I calculated their Riesel weight and the probability of there being a prime from their leading edge (~6.05M) to 10M.
k ; w ; Chance to 10M
2293 ; 0.1181815794 ; 8.56%
9221 ; 0.2101005857 ; 15.23%
23669 ; 0.090206229 ; 6.53%
31859 ; 0.097628261 ; 7.07%
38473 ; 0.059947178 ; 4.34%
40597 ; 0.151866184 ; 11.00%
46663 ; 0.065656433 ; 4.76%
67117 ; 0.111330473 ; 8.07%
74699 ; 0.050812369 ; 3.68%
81041 ; 0.065656433 ; 4.76%
93839 ; 0.160430066 ; 11.63%
97139 ; 0.078216794 ; 5.67%
107347 ; 0.11418510 ; 8.27%
121889 ; 0.08506790 ; 6.16%
129007 ; 0.05994717 ; 4.34%
143047 ; 0.05138329 ; 3.72%
146561 ; 0.10961769 ; 7.94%
161669 ; 0.03368460 ; 2.44%
192971 ; 0.03653923 ; 2.64%
206039 ; 0.07992957 ; 5.79%
206231 ; 0.07364939 ; 5.33%
215443 ; 0.11589787 ; 8.40%
226153 ; 0.08449697 ; 6.12%
234343 ; 0.08963530 ; 6.49%
245561 ; 0.02740442 ; 1.98%
250027 ; 0.06736920 ; 4.88%
273809 ; 0.11304324 ; 8.19%
304207 ; 0.03653923 ; 2.64%
315929 ; 0.11703972 ; 8.48%
319511 ; 0.15985914 ; 11.58%
324011 ; 0.08963530 ; 6.49%
325123 ; 0.07307846 ; 5.29%
327671 ; 0.05937625 ; 4.30%
336839 ; 0.22323187 ; 16.18%
342847 ; 0.01998239 ; already at 10M
344759 ; 0.09648641 ; 6.99%
362609 ; 0.15414988 ; 11.17%
363343 ; 0.09020622 ; 6.53%
364903 ; 0.15357896 ; 11.13%
365159 ; 0.14273137 ; 10.34%
368411 ; 0.15414988 ; 11.17%
371893 ; 0.09534455 ; 6.91%
384539 ; 0.10733399 ; 7.78%
386801 ; 0.06908198 ; 5.00%
397027 ; 0.04852866 ; 3.51%
398023 ; 0.07307846 ; 5.29%
402539 ; 0.13416749 ; 9.72%
409753 ; 0.10048288 ; 7.28%
444637 ; 0.02169516 ; already at 10M
470173 ; 0.09134808 ; 6.62%
474491 ; 0.14786970 ; 10.72%
477583 ; 0.03311367 ; 2.40%
485557 ; 0.05252514 ; 3.80%
494743 ; 0.05366699 ; 3.89%
502573 ; 0.06337273 ; 4.59%
According to this we will, on average, find primes for 3.6 k's below n=10M.
342847 and 444637 have already been pushed to 10M, presumably because they have the lowest number of tests remaining after sieving. However they also have the lowest chance of finding a prime.
9221 and 336839 have the highest chance of finding a prime. Does anyone else feel like we should be attacking those k's first?

Note that my chance calculation is based on the Prime Number theory:
http://www.primegrid.com/forum_thread.php?id=4935&nowrap=true#64017
____________

Janita
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Joined: 5 Feb 09
Posts: 16
ID: 35144
Credit: 45,153,803
RAC: 2,995
Discovered 1 mega primeEliminated 1 conjecture "k"321 LLR Gold: Earned 500,000 credits (759,760)Cullen LLR Gold: Earned 500,000 credits (735,129)ESP LLR Ruby: Earned 2,000,000 credits (2,291,603)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,799,897)PPS LLR Ruby: Earned 2,000,000 credits (3,109,725)PSP LLR Ruby: Earned 2,000,000 credits (2,058,559)SoB LLR Ruby: Earned 2,000,000 credits (2,348,190)SR5 LLR Ruby: Earned 2,000,000 credits (4,168,935)SGS LLR Amethyst: Earned 1,000,000 credits (1,309,757)TRP LLR Jade: Earned 10,000,000 credits (11,071,214)Woodall LLR Gold: Earned 500,000 credits (949,516)321 Sieve Ruby: Earned 2,000,000 credits (2,159,514)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (20,463)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,020,794)PPS Sieve Turquoise: Earned 5,000,000 credits (5,783,805)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (504,488)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,151,537)AP 26/27 Silver: Earned 100,000 credits (112,990)GFN Amethyst: Earned 1,000,000 credits (1,169,053)PSA Amethyst: Earned 1,000,000 credits (1,628,813)
Message 65987 - Posted: 27 May 2013 | 17:33:36 UTC - in response to Message 65923.

I think it would be interesting to see which k's you would have preferred if you would have calculated the probabilities of all of the original 64 candidates in the n-range of 3M to 10M. If your prediction would have resulted in more hits than falses with respect to the nine primes we have found so far it could be worthwile to push two of the k's forward at higher speed. But I remember that I have checked how many tests were avoided by the first finds and it were not the biggest numbers of tests for the deleted k so I guess your method has a good chance to fail. Anyway, the target of this TRP excercise is to prove that a prime exists for every remaining k. Therefore it does not really matter when they are found. But yes, it is time for another one as there was for so long no hit...

Profile Roger
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Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,530,863
RAC: 1,408
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,213,934)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)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 (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,515,310)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 66022 - Posted: 28 May 2013 | 11:54:12 UTC - in response to Message 65987.

For the TRP found k of the original 64:
k ; w ; rank(w) of 64 ; n found
65531 ; 0.1130432499 ; 18 ; 3.6M
123547 ; 0.062801805 ; 49 ; 4.2M
141941 ; 0.246068892 ; 01 ; 4.3M
162941 ; 0.073078464 ; 41 ; 5.0M
191249 ; 0.104479367 ; 23 ; 3.4M
252191 ; 0.085638825 ; 33 ; 5.5M
353159 ; 0.079358645 ; 38 ; 4.3M
415267 ; 0.171277651 ; 04 ; 4.2M
428639 ; 0.085638827 ; 34 ; 3.5M

Average rank = 26.7 => 41.8% of range

As a predictor it's not fabulous, but then it's still better than a random k (50% of range).
The first expected prime for k with w below 0.05 is really scary, like n in the billions, and it goes up super fast as w gets smaller.

Janita
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Joined: 5 Feb 09
Posts: 16
ID: 35144
Credit: 45,153,803
RAC: 2,995
Discovered 1 mega primeEliminated 1 conjecture "k"321 LLR Gold: Earned 500,000 credits (759,760)Cullen LLR Gold: Earned 500,000 credits (735,129)ESP LLR Ruby: Earned 2,000,000 credits (2,291,603)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,799,897)PPS LLR Ruby: Earned 2,000,000 credits (3,109,725)PSP LLR Ruby: Earned 2,000,000 credits (2,058,559)SoB LLR Ruby: Earned 2,000,000 credits (2,348,190)SR5 LLR Ruby: Earned 2,000,000 credits (4,168,935)SGS LLR Amethyst: Earned 1,000,000 credits (1,309,757)TRP LLR Jade: Earned 10,000,000 credits (11,071,214)Woodall LLR Gold: Earned 500,000 credits (949,516)321 Sieve Ruby: Earned 2,000,000 credits (2,159,514)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (20,463)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,020,794)PPS Sieve Turquoise: Earned 5,000,000 credits (5,783,805)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (504,488)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,151,537)AP 26/27 Silver: Earned 100,000 credits (112,990)GFN Amethyst: Earned 1,000,000 credits (1,169,053)PSA Amethyst: Earned 1,000,000 credits (1,628,813)
Message 66109 - Posted: 29 May 2013 | 17:04:52 UTC - in response to Message 66022.
Last modified: 29 May 2013 | 17:07:15 UTC

Interesting, your first place guess was in the list of found primes.
My curiosity lets me ask one more question: How many primes would you have anticipated at PrimeGrid's start of the TRP-project for the range of n=3M to n=6M?

Profile Roger
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Joined: 27 Nov 11
Posts: 1112
ID: 120786
Credit: 261,530,863
RAC: 1,408
Found 1 prime in the 2018 Tour de Primes321 LLR Ruby: Earned 2,000,000 credits (2,012,522)Cullen LLR Amethyst: Earned 1,000,000 credits (1,359,862)ESP LLR Ruby: Earned 2,000,000 credits (2,213,934)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,088,705)PPS LLR Ruby: Earned 2,000,000 credits (2,617,785)PSP LLR Ruby: Earned 2,000,000 credits (2,420,512)SoB LLR Amethyst: Earned 1,000,000 credits (1,780,064)SR5 LLR Ruby: Earned 2,000,000 credits (2,238,295)SGS LLR Ruby: Earned 2,000,000 credits (2,139,392)TRP LLR Ruby: Earned 2,000,000 credits (2,125,391)Woodall LLR Amethyst: Earned 1,000,000 credits (1,311,937)321 Sieve Turquoise: Earned 5,000,000 credits (5,190,731)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (207,387)Generalized Cullen/Woodall Sieve Turquoise: Earned 5,000,000 credits (5,049,697)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 (20,295,860)GFN Emerald: Earned 50,000,000 credits (56,515,310)PSA Sapphire: Earned 20,000,000 credits (43,298,465)
Message 66236 - Posted: 1 Jun 2013 | 6:27:21 UTC - in response to Message 66109.

For the original 64 k's would have expected to find, on average, 6.1 primes in the range 3M<n<6M.
We found 9 within that range.
The probability distribution would be some kind of bell curve and we were on the luckier end.

Janita
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Joined: 5 Feb 09
Posts: 16
ID: 35144
Credit: 45,153,803
RAC: 2,995
Discovered 1 mega primeEliminated 1 conjecture "k"321 LLR Gold: Earned 500,000 credits (759,760)Cullen LLR Gold: Earned 500,000 credits (735,129)ESP LLR Ruby: Earned 2,000,000 credits (2,291,603)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,799,897)PPS LLR Ruby: Earned 2,000,000 credits (3,109,725)PSP LLR Ruby: Earned 2,000,000 credits (2,058,559)SoB LLR Ruby: Earned 2,000,000 credits (2,348,190)SR5 LLR Ruby: Earned 2,000,000 credits (4,168,935)SGS LLR Amethyst: Earned 1,000,000 credits (1,309,757)TRP LLR Jade: Earned 10,000,000 credits (11,071,214)Woodall LLR Gold: Earned 500,000 credits (949,516)321 Sieve Ruby: Earned 2,000,000 credits (2,159,514)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (20,463)Generalized Cullen/Woodall Sieve Amethyst: Earned 1,000,000 credits (1,020,794)PPS Sieve Turquoise: Earned 5,000,000 credits (5,783,805)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (504,488)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,151,537)AP 26/27 Silver: Earned 100,000 credits (112,990)GFN Amethyst: Earned 1,000,000 credits (1,169,053)PSA Amethyst: Earned 1,000,000 credits (1,628,813)
Message 66238 - Posted: 1 Jun 2013 | 7:19:56 UTC - in response to Message 66236.

If only one k would be pushed forward I would prefer 9221 as those tests run significantly faster on my computers.

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Joined: 12 Apr 11
Posts: 128
ID: 94709
Credit: 164,082,201
RAC: 5,606
321 LLR Amethyst: Earned 1,000,000 credits (1,081,800)ESP LLR Amethyst: Earned 1,000,000 credits (1,958,365)PPS LLR Ruby: Earned 2,000,000 credits (3,000,162)PSP LLR Amethyst: Earned 1,000,000 credits (1,022,562)SoB LLR Ruby: Earned 2,000,000 credits (2,015,539)SR5 LLR Ruby: Earned 2,000,000 credits (2,000,481)SGS LLR Ruby: Earned 2,000,000 credits (2,000,014)TRP LLR Ruby: Earned 2,000,000 credits (3,000,865)321 Sieve Ruby: Earned 2,000,000 credits (2,000,357)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,000,096)PPS Sieve Emerald: Earned 50,000,000 credits (50,000,422)TRP Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,500)AP 26/27 Sapphire: Earned 20,000,000 credits (20,000,721)GFN Sapphire: Earned 20,000,000 credits (20,000,117)PSA Emerald: Earned 50,000,000 credits (50,000,198)
Message 66239 - Posted: 1 Jun 2013 | 8:08:11 UTC - in response to Message 66238.
Last modified: 1 Jun 2013 | 8:08:54 UTC

If only one k would be pushed forward I would prefer 9221 as those tests run significantly faster on my computers.

n=6.1M (~6100000 bits)

k=2293 AVX FFT length 448K Time per bit: 1.961 ms.
k=9221 AVX FFT length 480K Time per bit: 2.127 ms.
k=23669 AVX FFT length 512K Time per bit: 2.195 ms.
...
k=107347 AVX FFT length 560K Time per bit: 2.506 ms.
...
k=502573 AVX FFT length 640K Time per bit: 2.894 ms.

Message boards : The Riesel Problem : Chance of TRP Prime

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