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

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  • 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 1 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 2 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 3 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 4 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 5 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 6 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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