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Re: [PrimeNumbers] Project to factorise F9(10)?

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  • Phil Carmody
    ... It s always worth flinging such numbers at ECM. This should give you hope, assuming you have access to lots of MIPS:
    Message 1 of 6 , Nov 16, 2012
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      --- On Fri, 11/16/12, julienbenney <jpbenney@...> wrote:
      > Regarding the question of Fermat
      > factorisation, one question that has interested me is the
      > factorisation of the ninth generalised Fermat number in base
      > ten, or 10^512+1 in more conventional notation.
      >
      > This number has three known prime factors in 1514497,
      > 302078977 and 3611707318387778163302401, plus a 473-digit
      > composite factor. Of the known factors, the 25-digit and
      > largest factor was found twelve years ago, and I do not know
      > how much further F9(10) has been searched since 2000.
      >
      > I wonder if there is any possibility that the complete
      > factorisation of F9(10) could be done in the future and
      > whether it would be worth more effort than it is receiving
      > currently?

      It's always worth flinging such numbers at ECM.

      This should give you hope, assuming you have access to lots of MIPS:

      http://www.loria.fr/~zimmerma/records/top50.html
      """
      1 79 2302872188505279576573535015926441913945044975483579529517513795897664211127797 11^306+1 800e6 3648110021 2012-Aug-12 S. Wagstaff
      """
      Shame on everyone who heard of this, and didn't report it on - wow!

      Phil
    • djbroadhurst
      ... Here is the press statement: http://homes.cerias.purdue.edu/~ssw/cun/press/tech.html David
      Message 2 of 6 , Nov 16, 2012
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        --- In primenumbers@yahoogroups.com,
        Phil Carmody <thefatphil@...> wrote:

        > This should give you hope, assuming you have access
        > to lots of MIPS:
        > http://www.loria.fr/~zimmerma/records/top50.html

        Here is the press statement:
        http://homes.cerias.purdue.edu/~ssw/cun/press/tech.html

        David
      • pbtoau
        GIMPS reported a 143 digit factor of M1061 found using ECM on 04AUG2012
        Message 3 of 6 , Nov 17, 2012
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          GIMPS reported a 143 digit factor of M1061 found using ECM on 04AUG2012

          --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:
          >
          > --- On Fri, 11/16/12, julienbenney <jpbenney@...> wrote:
          > > Regarding the question of Fermat
          > > factorisation, one question that has interested me is the
          > > factorisation of the ninth generalised Fermat number in base
          > > ten, or 10^512+1 in more conventional notation.
          > >
          > > This number has three known prime factors in 1514497,
          > > 302078977 and 3611707318387778163302401, plus a 473-digit
          > > composite factor. Of the known factors, the 25-digit and
          > > largest factor was found twelve years ago, and I do not know
          > > how much further F9(10) has been searched since 2000.
          > >
          > > I wonder if there is any possibility that the complete
          > > factorisation of F9(10) could be done in the future and
          > > whether it would be worth more effort than it is receiving
          > > currently?
          >
          > It's always worth flinging such numbers at ECM.
          >
          > This should give you hope, assuming you have access to lots of MIPS:
          >
          > http://www.loria.fr/~zimmerma/records/top50.html
          > """
          > 1 79 2302872188505279576573535015926441913945044975483579529517513795897664211127797 11^306+1 800e6 3648110021 2012-Aug-12 S. Wagstaff
          > """
          > Shame on everyone who heard of this, and didn't report it on - wow!
          >
          > Phil
          >
        • djbroadhurst
          ... No. That would really would be turning lead into gold :-) In fact this impressive factorization was done with SNFS, not ECM:
          Message 4 of 6 , Nov 17, 2012
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            --- In primenumbers@yahoogroups.com,
            "pbtoau" <PbtoAu@...> wrote:

            > GIMPS reported a 143 digit factor of M1061 found using
            > ECM on 04AUG2012

            No. That would really would be turning lead into gold :-)
            In fact this impressive factorization was done with SNFS, not ECM:

            http://eprint.iacr.org/2012/444.pdf

            David
          • pbtoau
            David, It sounded too good to be true, not unlike alchemy (good catch on the ID). This is where I got the info
            Message 5 of 6 , Nov 17, 2012
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              David,

              It sounded too good to be true, not unlike alchemy (good catch on the ID). This is where I got the info "http://www.mersenne.ca/stats.php?showuserstats=*". It erroneously credits ECM in two places for the factorization.

              WBR,

              DB

              --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
              >
              >
              >
              > --- In primenumbers@yahoogroups.com,
              > "pbtoau" <PbtoAu@> wrote:
              >
              > > GIMPS reported a 143 digit factor of M1061 found using
              > > ECM on 04AUG2012
              >
              > No. That would really would be turning lead into gold :-)
              > In fact this impressive factorization was done with SNFS, not ECM:
              >
              > http://eprint.iacr.org/2012/444.pdf
              >
              > David
              >
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