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Message boards : Project Staging Area : Sophie Germain sieve

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Profile warddrProject donor
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Joined: 7 Feb 08
Posts: 254
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Credit: 9,878,813
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PPS LLR Ruby: Earned 2,000,000 credits (2,315,064)SGS LLR Ruby: Earned 2,000,000 credits (2,113,266)TPS LLR (retired) Bronze: Earned 10,000 credits (20,542)321 Sieve (suspended) Silver: Earned 100,000 credits (111,333)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (20,009)PPS Sieve Ruby: Earned 2,000,000 credits (3,020,844)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,056,728)TRP Sieve (suspended) Silver: Earned 100,000 credits (169,622)AP 26/27 Silver: Earned 100,000 credits (107,843)GFN Silver: Earned 100,000 credits (332,060)PSA Gold: Earned 500,000 credits (606,099)
Message 15999 - Posted: 2 Jun 2009 | 18:51:30 UTC

Small question, how and how much is the Sophie Germain range sieved?
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JohnProject donor
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321 LLR Bronze: Earned 10,000 credits (11,773)Cullen LLR Bronze: Earned 10,000 credits (14,945)ESP LLR Bronze: Earned 10,000 credits (26,855)PPS LLR Bronze: Earned 10,000 credits (84,876)PSP LLR Bronze: Earned 10,000 credits (15,311)SoB LLR Bronze: Earned 10,000 credits (21,440)SR5 LLR Bronze: Earned 10,000 credits (29,270)SGS LLR Bronze: Earned 10,000 credits (26,616)TPS LLR (retired) Bronze: Earned 10,000 credits (36,288)TRP LLR Bronze: Earned 10,000 credits (41,655)Woodall LLR Bronze: Earned 10,000 credits (15,807)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,014)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (23,405)PPS Sieve Bronze: Earned 10,000 credits (36,192)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (20,306)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,738)GFN Bronze: Earned 10,000 credits (86,217)PSA Ruby: Earned 2,000,000 credits (2,143,756)
Message 16002 - Posted: 2 Jun 2009 | 19:08:03 UTC - in response to Message 15999.

Small question, how and how much is the Sophie Germain range sieved?

We used David Underbakke's TwinGen. Sieving was completed in Jan 2008. Below is some additional information:

  • Sophie Germain Prime Search
    A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. For example, 5 is a Sophie Germain prime because it is prime and 2 × 5 + 1 = 11, is also prime. They are named after Marie-Sophie Germain, an extraordinary French mathematician.

    We'll be searching the form k*2^n-1. If it is prime, then we'll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1. We are able to do this because a quad sieve was performed for this search. This sieve ensured that k*2^n-1, k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1 do not have any small prime divisors.

    As you can see, a twin prime is also possible from this search although we expect to find a Sophie Germain prime first. Here are some stats for the search:

    k range: 1<k<41T
    n=666666
    sieve depth: p=200T
    candidates remaining: 34,190,344

    Probability of one or more significant pair = 80.1%
    Probability of one or more SG = 66.7%
    Probability of one or more Twin = 42.3%

    Approximate WU length:
    Athlon64 2.1Ghz - ~2000 secs (~33.3 minutes)
    C2D 2.1 Ghz - ~1015 secs (~16.9 minutes) per core
    C2Q 2.4 GHz - ~880 secs (~14.7 minutes) per core

    For more information about Sophie Germain primes, please visit these links:
    http://primes.utm.edu/glossary/page.php?sort=SophieGermainPrime
    http://mathworld.wolfram.com/SophieGermainPrime.html
    http://en.wikipedia.org/wiki/Sophie_Germain_prime

    For more infomation about Marie-Sophie Germain, please visit these links:
    http://en.wikipedia.org/wiki/Sophie_Germain
    http://www.pbs.org/wgbh/nova/proof/germain.html


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Credit: 296,361
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PPS LLR Bronze: Earned 10,000 credits (19,009)SR5 LLR Bronze: Earned 10,000 credits (11,940)PPS Sieve Bronze: Earned 10,000 credits (15,104)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (49,769)PSA Silver: Earned 100,000 credits (182,998)
Message 16021 - Posted: 3 Jun 2009 | 14:49:55 UTC

This depth is ENOUGH already?

Message boards : Project Staging Area : Sophie Germain sieve

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