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

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  • Mark Rodenkirch
    ... primeform? That s ancient. I presume you mean pfgw. --Mark
    Message 1 of 9 , Sep 1, 2011
      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 2 of 9 , Sep 1, 2011
        --- 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 3 of 9 , Sep 1, 2011
          >> 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 4 of 9 , Sep 1, 2011
            --- 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 5 of 9 , Sep 1, 2011
              --- 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 6 of 9 , Sep 1, 2011
                --- 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 7 of 9 , Sep 2, 2011
                  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 8 of 9 , Sep 2, 2011
                    --- 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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