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5132 digit BLS provable AP5

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  • Ken Davis
    Hi All, My search for 5000 digit BLS provable CPAP#/triplets is nearing its end. Over the past 4.5 years I have used approx 20GHZ years processing primes of
    Message 1 of 2 , Feb 9, 2007
      Hi All,
      My search for >5000 digit BLS provable CPAP#/triplets is nearing its
      end.
      Over the past 4.5 years I have used approx 20GHZ years processing
      primes of the type
      (N*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      I have prped over 90,000,000 numbers.
      Found 276228 prps which contained 2562 pairs (+7 and one of +1 +5 +11
      and +13)
      (8 triples (2CPAP3's,4 triplets and 2 of no use)
      As a sub search I started looking for arithmetic progressions.
      I have found
      2123751 AP3s
      2173 Ap4s
      and 2 ( the second one being the reason for this post) AP5's.
      (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      + N*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35)
      is prime for N=(0-4)

      All proofs used -tp
      additional -xvalues were required for N=1 and N=3

      Primality testing (49077426729*205881*4001#*(205881*4001#+1)+210)*
      (205881*4001#-1)/35+7 +

      0*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) [N-1,
      Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 3
      Running N-1 test using base 5
      Calling Brillhart-Lehmer-Selfridge with factored part 33.35%
      (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      + 0*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) is

      prime! (27.2622s+0.1807s)

      Using -x8177729

      Primality testing (49077426729*205881*4001#*(205881*4001#+1)+210)*
      (205881*4001#-1)/35+7 +

      1*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) [N-
      1/N+1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 3
      Running N-1 test using base 5
      Running N-1 test using base 11
      Running N+1 test using discriminant 19, base 1+sqrt(19)
      Calling N-1 BLS with factored part 33.25% and helper 0.11% (99.87%
      proof)
      1/571185908
      8193/571185908
      16385/571185908
      lots of lines removed
      8167425/571185908
      8175617/571185908
      (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      + 1*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) is

      prime! (1722.9017s+0.0469s)

      Primality testing (49077426729*205881*4001#*(205881*4001#+1)+210)*
      (205881*4001#-1)/35+7 +

      2*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) [N-
      1/N+1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 23
      Running N-1 test using base 31
      Running N+1 test using discriminant 43, base 3+sqrt(43)
      Calling N-1 BLS with factored part 33.37% and helper 0.02% (100.13%
      proof)
      (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      + 2*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) is

      prime! (40.5022s+0.2313s)

      using -x76085

      Primality testing (49077426729*205881*4001#*(205881*4001#+1)+210)*
      (205881*4001#-1)/35+7 +

      3*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) [N-
      1/N+1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 3
      Running N+1 test using discriminant 11, base 2+sqrt(11)
      Calling N-1 BLS with factored part 33.27% and helper 0.09% (99.91%
      proof)
      1/1034114599
      8193/1034114599
      16385/1034114599
      a few lines removed
      65537/1034114599
      73729/1034114599
      (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      + 3*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) is

      prime! (53.8161s+0.0648s)

      Primality testing (49077426729*205881*4001#*(205881*4001#+1)+210)*
      (205881*4001#-1)/35+7 +

      4*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) [N-
      1/N+1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 59
      Running N-1 test using base 67
      Running N+1 test using discriminant 79, base 4+sqrt(79)
      Calling N-1 BLS with factored part 33.34% and helper 0.11% (100.15%
      proof)
      (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
      + 4*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35) is

      prime! (39.7342s+0.3566s)

      I plan to finish up my search by extending the 2123751 AP3's to see
      if I can find any more Ap5s then I'll start a new project.
      Cheers
      Ken
    • Jens Kruse Andersen
      ... Congratulations on the results of this massive effort. The new AP5 record is at http://hjem.get2net.dk/jka/math/aprecords.htm which also contains many
      Message 2 of 2 , Feb 9, 2007
        Ken Davis wrote:
        > My search for >5000 digit BLS provable CPAP#/triplets is nearing
        > its end.
        > Over the past 4.5 years I have used approx 20GHZ years

        > (49077426729*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7
        > + N*(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35)
        > is prime for N=(0-4)

        Congratulations on the results of this massive effort.
        The new AP5 record is at http://hjem.get2net.dk/jka/math/aprecords.htm
        which also contains many recent long AP records by Jaroslaw Wroblewski.

        Thanks for including APTreeSieve in the Prime Pages prover code.
        Sorry I haven't made a publicly available version.
        It may still happen at some time if there is interest.

        --
        Jens Kruse Andersen
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