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Re: [PrimeNumbers] 11593 digit sexy prime pair

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  • 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 1 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 2 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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