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46157*2^698207+1

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  • David Broadhurst
    [Please note new title, for change of focus.] We do not yet know whether 46157*2^698207+1 is a Keller prime [not yet proven] i.e. whether 46157*2^n+1 is
    Message 1 of 8 , Dec 2, 2002
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      [Please note new title, for change of focus.]

      We do not yet know whether

      46157*2^698207+1 is a Keller prime [not yet proven]

      i.e. whether 46157*2^n+1 is composite for all
      natural n<698207, as well as being prime for n=698207.
      [The odds are very good!]

      The eventual announcement of that proof (or otherwise)
      will, one trusts, acknowledge the role played by
      Wilfrid Keller and Ian Lowman, among others.

      I reserve my congratulations, to all concerned,
      until such a proof is completed, since the original
      intent of the Sierpinski project, as I understand it,
      has not yet been fulfilled for k=46157.

      David (trying to be even handed)
    • Pavlos N
      46157*2^698207+1 is prime! (a=3) [210186 digits] 46157*2^698207+1 is prime! (a=5) [210186 digits] I havent completed the Generalized Fermat divisibility test
      Message 2 of 8 , Dec 3, 2002
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        46157*2^698207+1 is prime! (a=3) [210186 digits]
        46157*2^698207+1 is prime! (a=5) [210186 digits]
        I havent completed the Generalized Fermat divisibility
        test yet.Still 5 hours remaining
        Regards
        Pavlos
        --- David Broadhurst <d.broadhurst@...> wrote:
        > [Please note new title, for change of focus.]
        >
        > We do not yet know whether
        >
        > 46157*2^698207+1 is a Keller prime [not yet proven]
        >
        > i.e. whether 46157*2^n+1 is composite for all
        > natural n<698207, as well as being prime for
        > n=698207.
        > [The odds are very good!]
        >
        > The eventual announcement of that proof (or
        > otherwise)
        > will, one trusts, acknowledge the role played by
        > Wilfrid Keller and Ian Lowman, among others.
        >
        > I reserve my congratulations, to all concerned,
        > until such a proof is completed, since the original
        > intent of the Sierpinski project, as I understand
        > it,
        > has not yet been fulfilled for k=46157.
        >
        > David (trying to be even handed)
        >
        >
        >


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      • David Broadhurst
        ... That was not at issue. ... and explained what I meant ... as in W. Keller, The least prime of the form k.2n + 1 for certain values of k, ....^^^^ Abstracts
        Message 3 of 8 , Dec 3, 2002
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          Pavlos wrote:

          > 46157*2^698207+1 is prime! (a=5) [210186 digits]

          That was not at issue.

          Rather, I wrote:

          > We do not yet know whether
          > 46157*2^698207+1 is a Keller prime [not yet proven]

          and explained what I meant

          > i.e. whether 46157*2^n+1 is composite for all
          > natural n<698207, as well as being prime for
          > n=698207.

          as in

          W. Keller,
          The least prime of the form k.2n + 1 for certain values of k,
          ....^^^^
          Abstracts Amer. Math. Soc. 9 (1988), 417-418.

          I believe that for k=46157
          only a few exponents n<698207
          remain unanalyzed, at first pass.

          David
        • Pavlos N
          Ok.It is clear now. I finished the GF divisibility test. 46157*2^698207 + 1 is prime! (a = 3) [210186 digits] 46157*2^698207 + 1 is prime! (verification : a =
          Message 4 of 8 , Dec 3, 2002
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            Ok.It is clear now.
            I finished the GF divisibility test.
            46157*2^698207 + 1 is prime! (a = 3) [210186 digits]
            46157*2^698207 + 1 is prime! (verification : a = 5)
            [210186 digits]
            46157*2^698207 + 1 doesn't divide any Fm.
            46157*2^698207 + 1 doesn't divide any GF(3, m).
            46157*2^698207 + 1 doesn't divide any GF(5, m).
            46157*2^698207 + 1 doesn't divide any GF(6, m).
            46157*2^698207 + 1 doesn't divide any GF(10, m).
            46157*2^698207 + 1 doesn't divide any GF(12, m).
            46157*2^698207 - 1 factor : 3
            46157*2^698208 + 3 factor : 5
            46157*2^698208 + 1 factor : 3
            46157*2^698206 + 1 factor : 3
            Done.

            --- David Broadhurst <d.broadhurst@...> wrote:
            > Pavlos wrote:
            >
            > > 46157*2^698207+1 is prime! (a=5) [210186 digits]
            >
            > That was not at issue.
            >
            > Rather, I wrote:
            >
            > > We do not yet know whether
            > > 46157*2^698207+1 is a Keller prime [not yet
            > proven]
            >
            > and explained what I meant
            >
            > > i.e. whether 46157*2^n+1 is composite for all
            > > natural n<698207, as well as being prime for
            > > n=698207.
            >
            > as in
            >
            > W. Keller,
            > The least prime of the form k.2n + 1 for certain
            > values of k,
            > ....^^^^
            > Abstracts Amer. Math. Soc. 9 (1988), 417-418.
            >
            > I believe that for k=46157
            > only a few exponents n<698207
            > remain unanalyzed, at first pass.
            >
            > David
            >
            >
            >


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          • Payam Samidoost
            ... I have just finished my search for a GF(m,b) dividing 46157*2^698207+1. And here is the result: It divides none of the GF(m,b) with 19-smooth bases less
            Message 5 of 8 , Dec 3, 2002
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              > Ok.It is clear now.
              > I finished the GF divisibility test.
              > 46157*2^698207 + 1 is prime! (a = 3) [210186 digits]
              > 46157*2^698207 + 1 is prime! (verification : a = 5)
              > [210186 digits]
              > 46157*2^698207 + 1 doesn't divide any Fm.
              > 46157*2^698207 + 1 doesn't divide any GF(3, m).
              > 46157*2^698207 + 1 doesn't divide any GF(5, m).
              > 46157*2^698207 + 1 doesn't divide any GF(6, m).
              > 46157*2^698207 + 1 doesn't divide any GF(10, m).
              > 46157*2^698207 + 1 doesn't divide any GF(12, m).
              > 46157*2^698207 - 1 factor : 3
              > 46157*2^698208 + 3 factor : 5
              > 46157*2^698208 + 1 factor : 3
              > 46157*2^698206 + 1 factor : 3
              > Done.

              I have just finished my search for a GF(m,b) dividing 46157*2^698207+1. And here is the result:

              It divides none of the GF(m,b) with 19-smooth bases less than 200000.

              Note that Yves's Proth.exe which is used by Pavlos checks only the 5-smooth bases less than 13.

              Payam

              PS. keep visiting http://www.seventeenorbust.com in the next few hours to see the big news as soon as possible.



              [Non-text portions of this message have been removed]
            • David Broadhurst
              Payam: Did I just detect a FoB warning :-? David
              Message 6 of 8 , Dec 3, 2002
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                Payam: Did I just detect a FoB warning :-? David
              • Payam Samidoost
                ... Payam [Non-text portions of this message have been removed]
                Message 7 of 8 , Dec 3, 2002
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                  Oh, a small mistake in my previous post:

                  > my search for a GF(m,b) dividing 46157*2^698207+1.

                  corrected as:

                  > my search for a GF(m,b) divisible by 46157*2^698207+1.

                  Payam



                  [Non-text portions of this message have been removed]
                • gchil0
                  Can he call it or what? :-)
                  Message 8 of 8 , Dec 3, 2002
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                    Can he call it or what? :-)

                    --- In primenumbers@y..., "David Broadhurst" <d.broadhurst@o...> wrote:
                    > Payam: Did I just detect a FoB warning :-? David
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