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Message boards : Sophie Germain Prime Search : The Exponent

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Profile Gary Craig
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Joined: 30 Dec 09
Posts: 3186
ID: 52890
Credit: 953,169,624
RAC: 409,033
Discovered 1 mega prime321 LLR Ruby: Earned 2,000,000 credits (2,893,273)Cullen LLR Ruby: Earned 2,000,000 credits (2,440,687)ESP LLR Turquoise: Earned 5,000,000 credits (5,738,876)Generalized Cullen/Woodall LLR Turquoise: Earned 5,000,000 credits (6,292,626)PPS LLR Turquoise: Earned 5,000,000 credits (7,969,722)PSP LLR Turquoise: Earned 5,000,000 credits (5,653,927)SoB LLR Turquoise: Earned 5,000,000 credits (8,873,870)SR5 LLR Turquoise: Earned 5,000,000 credits (5,040,727)SGS LLR Ruby: Earned 2,000,000 credits (3,335,673)TRP LLR Jade: Earned 10,000,000 credits (12,547,399)Woodall LLR Ruby: Earned 2,000,000 credits (2,282,622)321 Sieve Silver: Earned 100,000 credits (215,455)Cullen/Woodall Sieve (suspended) Emerald: Earned 50,000,000 credits (59,788,598)Generalized Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,143,068)PPS Sieve Double Gold: Earned 500,000,000 credits (524,673,938)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 Sapphire: Earned 20,000,000 credits (43,842,888)GFN Double Bronze: Earned 100,000,000 credits (176,852,067)PSA Emerald: Earned 50,000,000 credits (62,378,755)
Message 73588 - Posted: 18 Feb 2014 | 5:55:00 UTC

I'm curious as to the history of how the exponent was/is chosen for the various SGS (and twin prime search) ranges that we've searched over the years. I believe that TPS (before my time) searched n=333333, and SGS mostly did n=666666 and now n=1.29M. I believe the immediate answer is that there had been heavy sieving done, making LLR efficient to run on those ranges. But that of course just begs the question as to why those ranges had been heavily sieved. Is there something "special" about those n's (other than the repeated digits, of course), or would it be equally valid/productive to search n=314159 or n=987987 or n=1234567? Assuming the sieving were done for those n, of course.

I did find a board post from Lennart saying (in part) that n=1.29M keeps us under a particular FFT size threshold.

Just curious.

--Gary
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"I am he as you are he as you are me and we are all together"

87*2^3496188+1 is prime! (1052460 digits)
4 is not prime! (1 digit)

HonzaProject donor
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Joined: 15 Aug 05
Posts: 1846
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Credit: 2,650,003,218
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Discovered 6 mega primesEliminated 3 conjecture "k"sFound 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2018 Tour de Primes Mountain Stage2019 Tour de Primes largest primeFound 4 primes in the 2019 Tour de PrimesFound 1 mega prime in the 2019 Tour de PrimesFound 1 prime in the 2019 Tour de Primes Mountain Stage321 LLR Emerald: Earned 50,000,000 credits (53,741,535)Cullen LLR Emerald: Earned 50,000,000 credits (50,296,190)ESP LLR Emerald: Earned 50,000,000 credits (50,853,190)Generalized Cullen/Woodall LLR Emerald: Earned 50,000,000 credits (50,309,119)PPS LLR Double Bronze: Earned 100,000,000 credits (100,184,938)PSP LLR Sapphire: Earned 20,000,000 credits (48,702,237)SoB LLR Emerald: Earned 50,000,000 credits (67,865,553)SR5 LLR Emerald: Earned 50,000,000 credits (50,320,316)SGS LLR Sapphire: Earned 20,000,000 credits (31,106,443)TPS LLR (retired) Bronze: Earned 10,000 credits (43,033)TRP LLR Emerald: Earned 50,000,000 credits (57,441,313)Woodall LLR Emerald: Earned 50,000,000 credits (50,956,094)321 Sieve Emerald: Earned 50,000,000 credits (50,611,470)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,142,109)Generalized Cullen/Woodall Sieve (suspended) 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 Double Silver: Earned 200,000,000 credits (214,118,887)GFN Double Gold: Earned 500,000,000 credits (638,759,743)PSA Double Gold: Earned 500,000,000 credits (535,218,662)
Message 73590 - Posted: 18 Feb 2014 | 8:46:58 UTC

One reason is that you mentioned, particular FFT size threshold.

The other reason is that we want to keep SGS in Top5000 as long as possible, which needs to be considered together with PPSe progress.
New SGS primes are entering ~1700 place and pushing all PPSe primes down (entering 3000 - 3500). Once PPSe crosses 1290k (with leading edge being around 1248k), it will start pushing all SGS down.

btw, TPS was done also for n=195000.
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Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 973
ID: 306875
Credit: 11,517,616
RAC: 6,259
321 LLR Silver: Earned 100,000 credits (360,928)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Ruby: Earned 2,000,000 credits (2,486,479)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Bronze: Earned 10,000 credits (16,010)SGS LLR Bronze: Earned 10,000 credits (32,929)TRP LLR Bronze: Earned 10,000 credits (71,060)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (101,851)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
Message 90293 - Posted: 9 Dec 2015 | 0:44:58 UTC

Right now, the prime:

835738017*2^1290000 - 1 (2012 July 14)

is ranked 5350 on Caldwell's list, and the prime:

2400254545845*2^1290000 - 1 (2015 December 8)

is ranked 3349 there.

Of course almost all the primes in the list in between these two are also from this project. (One user, p199, seems to start from two primes found by this project, say k*2^1290000-1 and j*2^1290000-1 (with k<j), and then see if i*2^1290000-1 is also prime, where i = j+(j-k) = 2j-k is the next member of the arithmetic progression k,j,...)

If we are lucky that one of our finds will be the lower member of a twin, or a safe prime, or a Sophie Germain prime, our exponent 1290000 is still large enough to ensure that both that prime and the associated prime are in Top 5000 in their own rights.

/JeppeSN

Message boards : Sophie Germain Prime Search : The Exponent

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