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Message boards : 321 Prime Search : Task Length

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Profile dannyridel
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Joined: 3 Feb 19
Posts: 940
ID: 1097922
Credit: 24,761,601
RAC: 50,316
Discovered 1 mega prime321 LLR Gold: Earned 500,000 credits (506,806)Cullen LLR Silver: Earned 100,000 credits (112,212)ESP LLR Silver: Earned 100,000 credits (438,864)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,021,028)PPS LLR Ruby: Earned 2,000,000 credits (2,158,145)PSP LLR Gold: Earned 500,000 credits (616,940)SoB LLR Gold: Earned 500,000 credits (533,625)SR5 LLR Silver: Earned 100,000 credits (145,606)SGS LLR Gold: Earned 500,000 credits (630,714)TRP LLR Silver: Earned 100,000 credits (230,447)Woodall LLR Silver: Earned 100,000 credits (117,864)321 Sieve (suspended) Gold: Earned 500,000 credits (506,814)Generalized Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (30,033)PPS Sieve Ruby: Earned 2,000,000 credits (2,868,721)AP 26/27 Amethyst: Earned 1,000,000 credits (1,273,545)GFN Turquoise: Earned 5,000,000 credits (5,489,321)WW Turquoise: Earned 5,000,000 credits (7,708,000)PSA Silver: Earned 100,000 credits (373,034)
Message 151729 - Posted: 10 Oct 2021 | 2:58:27 UTC

Is there some sort of mathematical explanation to why 321 tasks are so much faster than other tasks of similar length/smaller length like ESP? Is it due to the uniquely small k size?
____________
My lucky number is 6219*2^3374198+1


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Joined: 2 Feb 08
Posts: 808
ID: 18447
Credit: 461,253,018
RAC: 420,395
Discovered 1 mega primeFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (5,080,964)Cullen LLR Turquoise: Earned 5,000,000 credits (5,303,125)ESP LLR Turquoise: Earned 5,000,000 credits (5,016,107)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (6,298,060)PPS LLR Sapphire: Earned 20,000,000 credits (20,405,460)PSP LLR Turquoise: Earned 5,000,000 credits (5,872,604)SoB LLR Turquoise: Earned 5,000,000 credits (7,347,189)SR5 LLR Turquoise: Earned 5,000,000 credits (5,011,984)SGS LLR Turquoise: Earned 5,000,000 credits (5,308,023)TPS LLR (retired) Silver: Earned 100,000 credits (103,523)TRP LLR Turquoise: Earned 5,000,000 credits (5,674,739)Woodall LLR Turquoise: Earned 5,000,000 credits (5,002,649)321 Sieve (suspended) Sapphire: Earned 20,000,000 credits (26,923,188)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,119,699)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,278,995)PPS Sieve Emerald: Earned 50,000,000 credits (50,357,616)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (4,080,177)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,221,054)AP 26/27 Emerald: Earned 50,000,000 credits (55,696,176)GFN Emerald: Earned 50,000,000 credits (93,924,013)WW Double Bronze: Earned 100,000,000 credits (100,012,000)PSA Sapphire: Earned 20,000,000 credits (34,214,582)
Message 151732 - Posted: 10 Oct 2021 | 14:45:35 UTC - in response to Message 151729.

pretty much, yes.
not only that the number being tested is a little smaller at the same n, but i believe that small k can also be more efficient in gwnum as well? or is it just a smaller FFT?
____________

Profile dannyridel
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Joined: 3 Feb 19
Posts: 940
ID: 1097922
Credit: 24,761,601
RAC: 50,316
Discovered 1 mega prime321 LLR Gold: Earned 500,000 credits (506,806)Cullen LLR Silver: Earned 100,000 credits (112,212)ESP LLR Silver: Earned 100,000 credits (438,864)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,021,028)PPS LLR Ruby: Earned 2,000,000 credits (2,158,145)PSP LLR Gold: Earned 500,000 credits (616,940)SoB LLR Gold: Earned 500,000 credits (533,625)SR5 LLR Silver: Earned 100,000 credits (145,606)SGS LLR Gold: Earned 500,000 credits (630,714)TRP LLR Silver: Earned 100,000 credits (230,447)Woodall LLR Silver: Earned 100,000 credits (117,864)321 Sieve (suspended) Gold: Earned 500,000 credits (506,814)Generalized Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (30,033)PPS Sieve Ruby: Earned 2,000,000 credits (2,868,721)AP 26/27 Amethyst: Earned 1,000,000 credits (1,273,545)GFN Turquoise: Earned 5,000,000 credits (5,489,321)WW Turquoise: Earned 5,000,000 credits (7,708,000)PSA Silver: Earned 100,000 credits (373,034)
Message 151737 - Posted: 10 Oct 2021 | 23:52:35 UTC - in response to Message 151732.

Ah ok, I'm still not so sure about how it actually happens that it is faster though...
____________
My lucky number is 6219*2^3374198+1


Profile BurProject donor
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Joined: 25 Feb 20
Posts: 509
ID: 1241833
Credit: 398,862,407
RAC: 894,181
321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,315,295)ESP LLR Ruby: Earned 2,000,000 credits (2,151,088)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,620,968)PPS LLR Turquoise: Earned 5,000,000 credits (6,471,655)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Ruby: Earned 2,000,000 credits (2,434,466)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Ruby: Earned 2,000,000 credits (2,027,649)TRP LLR Ruby: Earned 2,000,000 credits (2,089,856)Woodall LLR Ruby: Earned 2,000,000 credits (2,112,258)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Turquoise: Earned 5,000,000 credits (5,096,952)AP 26/27 Turquoise: Earned 5,000,000 credits (5,797,662)GFN Jade: Earned 10,000,000 credits (10,714,453)WW Double Silver: Earned 200,000,000 credits (345,684,000)PSA Amethyst: Earned 1,000,000 credits (1,042,601)
Message 151738 - Posted: 11 Oct 2021 | 6:16:05 UTC - in response to Message 151737.
Last modified: 11 Oct 2021 | 6:17:23 UTC

The prime test takes a specific amount of iterations that is proportional to the log of the tested number (i.e. the exponent). However, each iteration takes longer if the FFT size is large as in that case more multiplication steps are required per iteration. If you run llr2 manually you'll see it prints a "time per iteration", that increases with increasing FFT size.

The FFT size depends on both the size of the number and the size of k. And k=3 is the smallest one can get. You'll see that computation times for the different k's in the conjecture subprojects vary strongly depending on the respective k.

A short and more mathematical explanation can be found here:

Prime scores

As to why a large FFT requires more multiplications per iteration, I have no idea. Maybe some of the more knowledgeable members can explain that. :)
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,600,000

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Message boards : 321 Prime Search : Task Length

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