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RE: [PrimeNumbers] RE: Anyone like to prove primality of a Mersenne cofactor?

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  • Jon Perry
    How s the factorization of 2^(2^n)-1 coming along? Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/
    Message 1 of 7 , Mar 31, 2003
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      How's the factorization of 2^(2^n)-1 coming along?

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths/
      http://www.users.globalnet.co.uk/~perry/DIVMenu/
      BrainBench MVP for HTML and JavaScript
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    • Jon Perry
      Voodoo De Ja!!! Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP
      Message 2 of 7 , Mar 31, 2003
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      • Michael Bell
        Hi, Well I would do, but Primo doesn t seem to like wine. Has anyone had any success with that, or does anyone know of a Linux ECPP tool with comparable
        Message 3 of 7 , Apr 1, 2003
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          Hi,

          Well I would do, but Primo doesn't seem to like wine. Has anyone had any
          success with that, or does anyone know of a Linux ECPP tool with comparable
          speed?

          Mike.

          Paul Leyland wrote:
          > Will Edgington and I try to keep our tables of Mersenne factorizations
          > up to date by synchronizng every week or so. The latest indicated that
          > another Mersenne number had been completely factored. Neither Will nor
          > I have the resources at the moment to prove the 2193-digit cofactor of
          > M(7417) is prime. It's certainly a strong pseudoprime.
          >
          > If anyone would care to complete the proof, please let Will and me know
          > the result. The known prime factors of M(7417) are 118673, 16269026327
          > and 3888241452787718190543521.
          >
          > Apologies for not crediting the person who found the largest of the
          > three factors given above. I don't know who he or she is.
          >
          > Paul
          >
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        • David Broadhurst
          (2^7417-1)/(1930694161304071*3888241452787718190543521) 2193 c8 2002 Mersenne cofactor, ECPP
          Message 4 of 7 , Apr 1, 2003
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            (2^7417-1)/(1930694161304071*3888241452787718190543521) 2193 c8 2002
            Mersenne cofactor, ECPP
          • David Broadhurst
            These are the 6 smallest unproven probably prime Mersenne cofactors known to me: (2^14561-1)/8074991336582835391 (2^17029-1)/418879343
            Message 5 of 7 , Apr 1, 2003
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              These are the 6 smallest unproven probably prime
              Mersenne cofactors known to me:

              (2^14561-1)/8074991336582835391

              (2^17029-1)/418879343

              (2^20887-1)/(694257144641*3156563122511*28533972487913*\
              1893804442513836092687)

              (2^28759-1)/226160777

              (2^28771-1)/104726441

              (2^32531-1)/(65063*25225122959)

              Updates welcomed!

              David Broadhurst
            • jbrennen
              ... About as well as the factorization of 2^(2^n)+1 (the Fermat numbers). ... 2^(2^n)-1 == prod(i=0,n-1,2^(2^i)+1) So, completely factored up to 2^(2^12)-1.
              Message 6 of 7 , Apr 1, 2003
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                --- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:
                > How's the factorization of 2^(2^n)-1 coming along?

                About as well as the factorization of 2^(2^n)+1 (the Fermat numbers).

                :)


                2^(2^n)-1 == prod(i=0,n-1,2^(2^i)+1)


                So, completely factored up to 2^(2^12)-1.

                2^(2^13)-1, not yet factored.
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