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Message boards : Fermat Divisor Search : Computation times vary strongly

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Profile BurProject donor
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Credit: 279,915,382
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321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,002,841)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,202,156)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 (5,080,097)AP 26/27 Ruby: Earned 2,000,000 credits (4,665,622)GFN Turquoise: Earned 5,000,000 credits (7,489,336)WW Double Silver: Earned 200,000,000 credits (239,400,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 144531 - Posted: 21 Oct 2020 | 17:50:42 UTC

During the challenge I noticed that the computation times per task vary a lot. All computers are set single-threaded and one task per core (50% CPU on Host 1 to prevent HT).

Avg. / Min. / Max.
Host 1 (14 tasks / 24 h)
24,029 / 13,047 / 31,047

Host 2 (14 tasks / 24 h)
21,670 / 19,399 / 25,825

Host 3 (8 tasks / 24 h)
20,807 / 20,260 / 21,318

Host 1 is running GFN 17 mega simultaneously, but host 2 is more or less all the time idle and Host 3 which has the most constant values is actually my desktop computer. Does the time depend that strongly on k?

Furthermore, Host 1 is an i7-4790K, Host 2 is an i5-4590 and Host 3 is an i3-2120. I would have expected the i3 to be much slower, but it isn't.
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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Discovered the World's First base 116 Generalized Cullen prime!!!Discovered 28 mega primesEliminated 7 conjecture "k"sDiscovered 1 Sophie Germain pairDiscovered 2 Fermat divisors2012 Tour de Primes highest prime count2012 Tour de Primes most Mountain Stage primes2015 Tour de Primes highest prime count2016 Tour de Primes highest prime countFound 23 primes in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de PrimesFound 2 primes in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes highest prime countFound 22 primes in the 2019 Tour de Primes2020 Tour de Primes highest prime scoreFound 21 primes in the 2020 Tour de PrimesFound 4 mega primes in the 2020 Tour de PrimesFound 8 primes in the 2021 Tour de PrimesFound 1 mega prime in the 2021 Tour de Primes321 LLR Double Silver: Earned 200,000,000 credits (201,403,028)Cullen LLR Double Silver: Earned 200,000,000 credits (201,409,561)ESP LLR Double Silver: Earned 200,000,000 credits (214,825,147)Generalized Cullen/Woodall LLR Double Bronze: Earned 100,000,000 credits (131,911,637)PPS LLR Double Gold: Earned 500,000,000 credits (735,473,713)PSP LLR Double Bronze: Earned 100,000,000 credits (175,158,397)SoB LLR Double Silver: Earned 200,000,000 credits (207,028,068)SR5 LLR Double Silver: Earned 200,000,000 credits (214,437,634)SGS LLR Double Silver: Earned 200,000,000 credits (205,718,935)TPS LLR (retired) Silver: Earned 100,000 credits (235,439)TRP LLR Double Silver: Earned 200,000,000 credits (201,215,056)Woodall LLR Double Silver: Earned 200,000,000 credits (201,651,344)321 Sieve (suspended) Double Silver: Earned 200,000,000 credits (235,451,253)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (83,794,448)Generalized Cullen/Woodall Sieve (suspended) Double Silver: Earned 200,000,000 credits (285,139,652)PPS Sieve Double Ruby: Earned 2,000,000,000 credits (2,731,313,178)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Double Silver: Earned 200,000,000 credits (203,523,358)TRP Sieve (suspended) Double Silver: Earned 200,000,000 credits (201,489,157)AP 26/27 Double Silver: Earned 200,000,000 credits (438,154,574)GFN Double Ruby: Earned 2,000,000,000 credits (2,146,880,244)WW Double Ruby: Earned 2,000,000,000 credits (2,407,172,000)PSA Double Silver: Earned 200,000,000 credits (259,058,048)
Message 144534 - Posted: 21 Oct 2020 | 17:56:19 UTC - in response to Message 144531.


There are three different fft sizes currently being run on the DIV project: 384k, 400k, 480k. These will have longer run times, respectively.

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321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,002,841)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,202,156)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 (5,080,097)AP 26/27 Ruby: Earned 2,000,000 credits (4,665,622)GFN Turquoise: Earned 5,000,000 credits (7,489,336)WW Double Silver: Earned 200,000,000 credits (239,400,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 144556 - Posted: 22 Oct 2020 | 6:53:36 UTC - in response to Message 144534.
Last modified: 22 Oct 2020 | 6:53:53 UTC

Thanks, you're right, that was the cause. Surprisingly (to me) it's not the difference in n, which varied from 6.78 to 6.83, but the difference in k that causes FFT size to grow.

So large k will take much longer to compute while having marginal impact on the overall size of the prime?
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Gold: Earned 500,000 credits (611,298)ESP LLR Silver: Earned 100,000 credits (174,818)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Jade: Earned 10,000,000 credits (13,167,992)PSP LLR Silver: Earned 100,000 credits (428,457)SoB LLR Silver: Earned 100,000 credits (466,812)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (112,277)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve (suspended) Silver: Earned 100,000 credits (175,037)PPS Sieve Bronze: Earned 10,000 credits (10,113)AP 26/27 Bronze: Earned 10,000 credits (12,129)GFN Ruby: Earned 2,000,000 credits (2,059,478)WW Turquoise: Earned 5,000,000 credits (9,640,000)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 144558 - Posted: 22 Oct 2020 | 7:49:22 UTC - in response to Message 144556.

So large k will take much longer to compute while having marginal impact on the overall size of the prime?

Correct. Additionally, primes with larger k have smaller chances to be divisors of Fermat numbers and generalized Fermat numbers. /JeppeSN

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Credit: 279,915,382
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321 LLR Ruby: Earned 2,000,000 credits (2,092,823)Cullen LLR Ruby: Earned 2,000,000 credits (2,002,841)ESP LLR Amethyst: Earned 1,000,000 credits (1,445,099)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,180,764)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Ruby: Earned 2,000,000 credits (2,064,832)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Ruby: Earned 2,000,000 credits (2,065,004)SGS LLR Amethyst: Earned 1,000,000 credits (1,202,156)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 (5,080,097)AP 26/27 Ruby: Earned 2,000,000 credits (4,665,622)GFN Turquoise: Earned 5,000,000 credits (7,489,336)WW Double Silver: Earned 200,000,000 credits (239,400,000)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 144652 - Posted: 23 Oct 2020 | 16:15:24 UTC - in response to Message 144558.

I just realized that's exactly what the table posted by Kellen tells us.
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 4,800,000

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Message boards : Fermat Divisor Search : Computation times vary strongly

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