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An 85-digit AP13

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  • mikeoakes2
    Immediately after Ken announced his 83-digit AP13s in May: http://tech.groups.yahoo.com/group/primeform/message/10310 I resolved to continue our game of AP-k
    Message 1 of 3 , Dec 22, 2010
      Immediately after Ken announced his 83-digit AP13s in May:
      http://tech.groups.yahoo.com/group/primeform/message/10310
      I resolved to continue our game of AP-k leapfrog and retake the record.

      But it has been an uphill struggle.
      I spent 255 GHz-days failing to find one at 101 digits, and had to start over, with a more modest target.

      Finally, an AP13 with 85 digits turned up today:-

      (1296982250+14976848*n)*191#+1 is prime for n=0..12

      All confirmed prime with PFGW -tc

      Input/output statistics:-
      Numbers tested by NewPGen: 2*10^9
      NewPGen reduced these (by sieving to depth 150 billion) to: 4.1*10^8
      PRP's found by PFGW: 98 million
      AP12's found: 25
      AP13's found: 1

      Run-time statistics:-
      NewPGen: 8 GHz-hrs
      PFGW: 63 GHz-hrs
      Pascal program to find AP's: 331 GHz-days

      Poisson was clearly saving this up for Christmas: about 15 AP12's should have been enough to yield an AP13.

      Mike
    • Jens Kruse Andersen
      ... Congratulations! http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. -- Jens Kruse Andersen
      Message 2 of 3 , Dec 22, 2010
        Mike Oakes wrote:
        > (1296982250+14976848*n)*191#+1 is prime for n=0..12

        Congratulations!
        http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.

        --
        Jens Kruse Andersen
      • kraDen
        ... 101 digits was indeed ambitious. ... Congratulations. Looks like I have a new challenge for 2011. Though I hope to be spending a fair bit of resources
        Message 3 of 3 , Dec 23, 2010
          --- In primeform@yahoogroups.com, "mikeoakes2" <mikeoakes2@...> wrote:
          >
          > Immediately after Ken announced his 83-digit AP13s in May:
          > http://tech.groups.yahoo.com/group/primeform/message/10310
          > I resolved to continue our game of AP-k leapfrog and retake the record.
          >
          > But it has been an uphill struggle.
          > I spent 255 GHz-days failing to find one at 101 digits, and had to start over, with a more modest target.
          101 digits was indeed ambitious.
          >
          > Finally, an AP13 with 85 digits turned up today:-
          >
          > (1296982250+14976848*n)*191#+1 is prime for n=0..12
          >
          > All confirmed prime with PFGW -tc
          >
          > Input/output statistics:-
          > Numbers tested by NewPGen: 2*10^9
          > NewPGen reduced these (by sieving to depth 150 billion) to: 4.1*10^8
          > PRP's found by PFGW: 98 million
          > AP12's found: 25
          > AP13's found: 1
          >
          > Run-time statistics:-
          > NewPGen: 8 GHz-hrs
          > PFGW: 63 GHz-hrs
          > Pascal program to find AP's: 331 GHz-days
          >
          > Poisson was clearly saving this up for Christmas: about 15 AP12's should have been enough to yield an AP13.
          Congratulations.
          Looks like I have a new challenge for 2011.
          Though I hope to be spending a fair bit of resources particapting in the 1000 digit ap9 search.
          It also saves me working out which of the 16 83 digit ap13's I currently have is the largest.
          Currently at
          369 AP12's
          16 AP13's
          0 AP14's (you'll be among the first to know when I get lucky)
          cheers
          Ken
          > Mike
          >
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