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Project to factorise F9(10)?

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  • julienbenney
    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
    Message 1 of 6 , Nov 15, 2012
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      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?
    • 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 2 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 3 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 4 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 5 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 6 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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