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New Record for 13 simultaneous primes

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  • Dirk Augustin
    Hi all, after sieving through more than 10 trillion candidates to discover a new record Cunningham Chain of length 12, I surprisingly found a large Cunningham
    Message 1 of 2 , Dec 6, 2005
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      Hi all,
      after sieving through more than 10 trillion candidates to discover a
      new record Cunningham Chain of length 12, I surprisingly found a large
      Cunningham Chain of length 13:

      1753286498051*2^(n-1)*71#-1, n=1,..,13, (39 digits for n=1)

      This is also a new record for 13 simultaneous primes, where it counts
      with 41 digits (middle member of the chain), improving the old record
      by 8 digits.

      Regards,
      Dirk Augustin
    • Jens Kruse Andersen
      ... Congratulations! Longer than you searched again! http://hjem.get2net.dk/jka/math/Cunningham_Chain_records.htm and
      Message 2 of 2 , Dec 6, 2005
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        Dirk Augustin wrote:

        > Hi all,
        > after sieving through more than 10 trillion candidates to discover a
        > new record Cunningham Chain of length 12, I surprisingly found a large
        > Cunningham Chain of length 13:
        >
        > 1753286498051*2^(n-1)*71#-1, n=1,..,13, (39 digits for n=1)
        >
        > This is also a new record for 13 simultaneous primes, where it counts
        > with 41 digits (middle member of the chain), improving the old record
        > by 8 digits.

        Congratulations!
        Longer than you searched again!
        http://hjem.get2net.dk/jka/math/Cunningham_Chain_records.htm and
        http://hjem.get2net.dk/jka/math/simultprime.htm are updated.

        I see you used NewPGen+PFGW like on shorter CC's.
        I wonder how practical that is for 12 (and 13!) simultaneous primes.
        My sieve using the GMP library for prp'ing has 1 GHz week
        expected for a CC12 of this size.
        A CC13 would obviously have longer expectation for non-Dirks ;-)

        --
        Jens Kruse Andersen
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