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[PrimeNumbers] A PRP of the form 2*k*p +1

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  • Peter Lesala
    Keen to find prime factors of 2^333019 - 1, I went on to test 2*k*p + 1 for k = 10^100000. The test gives 2*(10^100000 + 50617) + 1 as a probable prime of
    Message 1 of 9 , Sep 1, 2011
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      Keen to find prime factors of 2^333019 - 1, I went on to test 2*k*p + 1 for k = 10^100000. The test gives

      2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits; using Primeform.

      Peter.

      [Non-text portions of this message have been removed]




      [Non-text portions of this message have been removed]
    • Mark Rodenkirch
      ... primeform? That s ancient. I presume you mean pfgw. --Mark
      Message 2 of 9 , Sep 1, 2011
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        On Sep 1, 2011, at 5:22 AM, Peter Lesala wrote:
        > Keen to find prime factors of 2^333019 - 1, I went on to test 2*k*p
        > + 1 for k = 10^100000. The test gives
        >
        > 2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits;
        > using Primeform.
        >
        primeform? That's ancient. I presume you mean pfgw.

        --Mark
      • Alan R Powell
        ... Peter Am I missing something, according to Mathematica: 2*(10^100000+50617) + 1 ends in a 5 2*(10^100000*50617) + 1 is divisible by 967 & 23473 Regards
        Message 3 of 9 , Sep 1, 2011
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          --- In primenumbers@yahoogroups.com, "Peter Lesala" <plesala@...> wrote:
          >
          > Keen to find prime factors of 2^333019 - 1, I went on to test 2*k*p + 1 for k = 10^100000. The test gives
          >
          > 2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits; using Primeform.
          >
          > Peter.
          >
          > [Non-text portions of this message have been removed]
          >
          >
          >
          >
          > [Non-text portions of this message have been removed]
          >
          Peter

          Am I missing something, according to Mathematica:

          2*(10^100000+50617) + 1 ends in a 5

          2*(10^100000*50617) + 1 is divisible by 967 & 23473

          Regards

          Alan
        • Maximilian Hasler
          ... no need to use Mathematica for that: 2*7 = 14 ; + 1 = 15 . Indeed a quite improbable prime. ... This I cannot confirm, according to PARI, divisors
          Message 4 of 9 , Sep 1, 2011
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            >> 2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits;

            >
            > Am I missing something, according to Mathematica:
            >
            >  2*(10^100000+50617) + 1 ends in a 5

            no need to use Mathematica for that:

            2*7 = 14 ; + 1 = 15 .

            Indeed a quite improbable prime.

            > 2*(10^100000*50617) + 1 is divisible by 967 & 23473

            This I cannot confirm, according to PARI, divisors < 5e5 are:
            5,36263 for 2*(10^100000+50617) + 1
            3,7,17,19 for 2*(10^100000+50617) - 1
            3,17,19,23473 for 2*(10^100000*50617) + 1
            11,167 for 2*(10^100000*50617) - 1

            But in fact the " * " versions don't make sense
            (why the "2" would be outside and 50617 inside the (...) ?)

            Maximilian
          • djbroadhurst
            ... Perhaps Peter meant to write something like 2*(10^100000+50617)*333019 + 1 David (looking at the title)
            Message 5 of 9 , Sep 1, 2011
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              --- In primenumbers@yahoogroups.com,
              "Alan R Powell" <AlanPowell@...> wrote:

              > > 2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits;
              > 2*(10^100000+50617) + 1 ends in a 5
              > 2*(10^100000*50617) + 1 is divisible by 967 & 23473

              Perhaps Peter meant to write something like

              2*(10^100000+50617)*333019 + 1

              David (looking at the title)
            • djbroadhurst
              ... according to OpenPFGW (2*(10^100000+50617)+1)/(5*36263*376504523) has no small factor. David
              Message 6 of 9 , Sep 1, 2011
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                --- In primenumbers@yahoogroups.com,
                Maximilian Hasler <maximilian.hasler@...> wrote:

                > according to PARI, divisors < 5e5 are:
                > 5,36263 for 2*(10^100000+50617) + 1

                according to OpenPFGW
                (2*(10^100000+50617)+1)/(5*36263*376504523) has no small factor.

                David
              • djbroadhurst
                ... It appears so: 2*(10^100000+50617)*333019+1 is 3-PRP! (1146.4749s+0.0010s) and hence may be Henrified. David
                Message 7 of 9 , Sep 1, 2011
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                  --- In primenumbers@yahoogroups.com,
                  "djbroadhurst" <d.broadhurst@...> wrote:

                  > Perhaps Peter meant to write something like
                  > 2*(10^100000+50617)*333019 + 1

                  It appears so:

                  2*(10^100000+50617)*333019+1 is 3-PRP! (1146.4749s+0.0010s)

                  and hence may be Henrified.

                  David
                • Peter Lesala
                  Really sorry for the clumsy mistake. I m indeed testing 2*k*p +1, and p=333019 is missing in the previous message. For interest s sake I found some two smaller
                  Message 8 of 9 , Sep 2, 2011
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                    Really sorry for the clumsy mistake. I'm indeed testing 2*k*p +1, and p=333019 is missing in the previous message. For interest's sake I found some two smaller PRPs before this one; i.e.

                    (1) 2*(10^10000+36107)*333019+1 is probable prime! (verification : a = 36761) (digits:10006)

                    (2) 2*(10^10000+49931)*333019+1 is probable prime! (verification : a = 36761) (digits:10006)

                    and then lately

                    (3) 2*(10^100000+50617)*333019+1 is probable prime! (verification : a = 42349) (digits:100006)

                    Thanks to David for the verification.

                    Peter.

                    ----- Original Message -----
                    From: Peter Lesala
                    To: primenumbers@yahoogroups.com ; Peter Lesala
                    Sent: Thursday, September 01, 2011 12:22 PM
                    Subject: [PrimeNumbers] A PRP of the form 2*k*p +1



                    Keen to find prime factors of 2^333019 - 1, I went on to test 2*k*p + 1 for k = 10^100000. The test gives

                    2*(10^100000 + 50617) + 1 as a probable prime of 100006 digits; using Primeform.

                    Peter.

                    [Non-text portions of this message have been removed]

                    [Non-text portions of this message have been removed]





                    [Non-text portions of this message have been removed]
                  • djbroadhurst
                    ... Might you tell us, please, Peter, why you chose to study this particular Mersenne exponent? ... Monna ya fetolang mmala ka nako le nako? Best regards David
                    Message 9 of 9 , Sep 2, 2011
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                      --- In primenumbers@yahoogroups.com,
                      "Peter Lesala" <plesala@...> wrote:

                      > Keen to find prime factors of 2^333019 - 1

                      Might you tell us, please, Peter, why you chose
                      to study this particular Mersenne exponent?

                      > p=333019 is missing in the previous message

                      Monna ya fetolang mmala ka nako le nako?

                      Best regards

                      David
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