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Unable to prove a PRP

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  • Bryan
    How can one prove the primality of a PRP when every program I ve tried is unable. To form of the prime is XYYX such as 2^2007+2007^2. I have many PRP s to
    Message 1 of 4 , Dec 12, 2006
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      How can one prove the primality of a PRP when every program I've tried
      is unable. To form of the prime is XYYX such as 2^2007+2007^2. I have
      many PRP's to check with the smallest being around 10k digits. Primo
      cannot handle the numbers and PFGW stops and complains that there are
      not enough factors. The switches, -t, -tp, -tc and -tm will not
      complete the proof. I've tried gmp-ecm and it seems like it'll take a
      few thousand years to run all the curves searching for factors. Anyone
      have any ideas?
    • Paul Underwood
      ... With a little less than 30% factorisation of N+1 and N-1 you can get a *proof* of primailty using PFGW plus CHG [1]. Otherwise a parallel implementation of
      Message 2 of 4 , Dec 12, 2006
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        --- In primenumbers@yahoogroups.com, "Bryan" <beyastard@...> wrote:
        >
        > How can one prove the primality of a PRP when every program I've tried
        > is unable. To form of the prime is XYYX such as 2^2007+2007^2. I have
        > many PRP's to check with the smallest being around 10k digits. Primo
        > cannot handle the numbers and PFGW stops and complains that there are
        > not enough factors. The switches, -t, -tp, -tc and -tm will not
        > complete the proof. I've tried gmp-ecm and it seems like it'll take a
        > few thousand years to run all the curves searching for factors. Anyone
        > have any ideas?
        >

        With a little less than 30% factorisation of N+1 and N-1 you can get a
        *proof* of primailty using PFGW plus CHG [1]. Otherwise a parallel
        implementation of ECPP such as FastECPP [2] would do, given you had
        the code and several networked computers,

        [1] http://tech.groups.yahoo.com/group/primeform/files/
        [2] http://primes.utm.edu/bios/page.php?id=689

        Can you tell us what the numbers are and how much factorisation of
        these you have achieved todate?

        Paul
      • jbrennen
        ... It looks like you could be rehashing stuff that s already been done: http://www.leyland.vispa.com/numth/primes/xyyx.htm Are you aware of that web page? A
        Message 3 of 4 , Dec 12, 2006
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          --- In primenumbers@yahoogroups.com, "Bryan" <beyastard@...> wrote:
          >
          > How can one prove the primality of a PRP when every program I've
          > tried is unable. To form of the prime is XYYX such as 2^2007+2007^2.
          > I have many PRP's to check with the smallest being around 10k digits.

          It looks like you could be rehashing stuff that's already been done:


          http://www.leyland.vispa.com/numth/primes/xyyx.htm

          Are you aware of that web page?

          A lot of PRPs there waiting for a proof...
        • Bryan
          ... 2^2007+2007^2. ... digits. ... Turns out I was rehashing some stuff. Using the list, I ve verified some of the PRPs needing a proof. Also, I ve been
          Message 4 of 4 , Dec 15, 2006
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            --- In primenumbers@yahoogroups.com, "jbrennen" <jb@...> wrote:
            >
            > --- In primenumbers@yahoogroups.com, "Bryan" <beyastard@> wrote:
            > >
            > > How can one prove the primality of a PRP when every program I've
            > > tried is unable. To form of the prime is XYYX such as
            2^2007+2007^2.
            > > I have many PRP's to check with the smallest being around 10k
            digits.
            >
            > It looks like you could be rehashing stuff that's already been
            done:
            >
            >
            > http://www.leyland.vispa.com/numth/primes/xyyx.htm
            >
            > Are you aware of that web page?
            >
            > A lot of PRPs there waiting for a proof...
            >
            Turns out I was rehashing some stuff. Using the list, I've verified
            some of the PRPs needing a proof. Also, I've been looking for
            ar2220.zip everywhere but cannot find it. Been wanting to rewrite
            VFYPR by Tony Forbes but lacking that file as it is no longer at his
            website. I'm at a standstill as I don't know what the fuctions do,
            don't know the structure of ireg, etc. Hopefully, someone out there
            has this file and will upload it to the files section of this group.
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