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11593 digit sexy prime pair

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  • Ken Davis
    Hi All, Not sure who (if anyone, as the Chris s prime pages doesn t track them) is interested in this type of prime but fyi
    Message 1 of 3 , May 5, 2009
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      Hi All,

      Not sure who (if anyone, as the Chris's prime pages doesn't track them) is interested in this type of prime but fyi

      ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5
      ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11

      are 11593 digit sexy prime pair.

      Primality testing ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 2
      Running N+1 test using discriminant 9029, base 1+sqrt(9029)
      Calling N+1 BLS with factored part 33.33% and helper 0.01% (99.99% proof)
      1/10
      ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5 is prime! (234.0480s+0.0032s)

      Primality testing ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11 [N+1, Brillhart-Lehmer-Selfridge]
      Running N+1 test using discriminant 3, base 3+sqrt(3)
      Calling Brillhart-Lehmer-Selfridge with factored part 33.32%
      Proof incomplete rerun with -x31194
      ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11 is Lucas PRP! (47.9885s+0.0033s)

      rerunning as instructed yields

      Primality testing ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11 [N+1, Brillhart-Lehmer-Selfridge]
      Running N+1 test using discriminant 3, base 3+sqrt(3)
      Calling Brillhart-Lehmer-Selfridge with factored part 33.32%
      1/31194
      8193/31194
      16385/31194
      24577/31194
      ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11 is prime! (56.3391s+0.0033s)
    • Jens Kruse Andersen
      ... Congrats. As far as I know, that is the largest proven pair, and the largest prp pairs are in http://mersenneforum.org/showthread.php?t=11381#10 I don t
      Message 2 of 3 , May 6, 2009
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        Ken Davis wrote:
        > Not sure who (if anyone, as the Chris's prime pages doesn't track them) is
        > interested in this type of prime but fyi
        >
        > ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5
        > ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11
        >
        > are 11593 digit sexy prime pair.

        Congrats. As far as I know, that is the largest proven pair, and the largest
        prp pairs are in http://mersenneforum.org/showthread.php?t=11381#10
        I don't think anybody is maintaining a record page.
        I only posted the former 11004-digit proven record to
        http://mersenneforum.org/showthread.php?t=11381#12

        --
        Jens Kruse Andersen
      • Ken Davis
        Hi All, A gigantic cousin pair (to go with the sexy pair) ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1
        Message 3 of 3 , May 8, 2009
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          Hi All,

          A gigantic cousin pair (to go with the sexy pair)

          ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1
          ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5

          with 11594 digitS

          Primality testing ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge]
          Running N-1 test using base 2
          Calling Brillhart-Lehmer-Selfridge with factored part 33.32%
          Proof incomplete rerun with -x41241
          ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 is PRP! (19.4720s+0.0029s)

          rerunning as instructed yields

          Primality testing ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge]
          Running N-1 test using base 2
          Calling Brillhart-Lehmer-Selfridge with factored part 33.32%
          1/41240
          8193/41240
          16385/41240
          24577/41240
          32769/41240
          40961/41240
          ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 is prime! (30.4132s+0.0024s)


          Primality testing ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
          Running N-1 test using base 9007
          Running N+1 test using discriminant 9013, base 1+sqrt(9013)
          Running N+1 test using discriminant 9013, base 2+sqrt(9013)
          Calling N+1 BLS with factored part 33.34% and helper 0.01% (100.02% proof)
          ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5 is prime! (279.4887s+0.0025s)

          Cheers
          Ken
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