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New big Fermat factor

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  • Leonid Durman
    Congratulations to Takahiro Nohara It is the big divider second after result Cosgrave for Fermat. Leonid Durman =============================== I found new
    Message 1 of 1 , Aug 5, 2003
      Congratulations to Takahiro Nohara
      It is the big divider second after result Cosgrave for Fermat.

      Leonid Durman

      ===============================
      I found new divisor of Fermat number.
      9*2^461081+1 divides F461076.

      I show the log of Proth.exe

      Mon Aug 04 09:24:01 2003 : Start: For n=461081 to 461081, For k=9 to 9 step
      2, k*2^n+1.
      Mon Aug 04 12:46:20 2003 : 9*2^461081 + 1 is prime! (a = 11) [138801 digits]
      Mon Aug 04 16:05:53 2003 : 9*2^461081 + 1 is prime! (verification : a = 19)
      [138801 digits]
      Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides F461076 !
      Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides GF(461077, 3) !
      Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides GF(461077, 6) !
      Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 divides GF(461077, 12) !
      Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 doesn't divide any GF(5, m).
      Tue Aug 05 16:10:27 2003 : 9*2^461081 + 1 doesn't divide any GF(10, m).
      Tue Aug 05 16:10:28 2003 : 9*2^461081 - 1 factor : 7
      Tue Aug 05 16:10:28 2003 : 9*2^461082 + 3 factor : 3
      Tue Aug 05 16:10:28 2003 : 9*2^461082 + 1 factor : 73
      Tue Aug 05 16:10:28 2003 : 9*2^461080 + 1 factor : 5
      Tue Aug 05 16:10:28 2003 : Done.

      I used NewPGen.exe and PRP.exe before Proth test.
      I've searched prime with form 9*2^n+1. This prime number is 4th of I ever
      found with same form.
      And this is second divisor of Fermat number found on my PCs.
      (My PCs are P3-600MHz*2.)

      I send same message to Payam Samidoost.
      Sorry, I can't send e-mail to Yahoo Group.
      I'll soon sign up to it.

      Best regards,
      Nohara
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