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Phi(N,2)

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  • Andrey Kulsha
    Hello! It would be interesting to collect all known factors of Phi(N,2) - primes Pn, probable primes PRPn, composites Cn and numbers Nn with unknown status -
    Message 1 of 4 , Oct 12, 2002
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      Hello!

      It would be interesting to collect all known factors of Phi(N,2) - primes Pn, probable primes PRPn, composites Cn and numbers Nn with unknown status - into one database. There are some information on Woltman's pages, Cunningham Project pages, Caldwell's Prime Pages, Lifchitz's PRP Top, our group archive, etc.

      Once it's done, some of us (maybe me?) would build a program which would show the percentage of factorizations of 2^N-1, 2^N+1 and Phi(N,2), largest and smallest factors of every type (P, PRP, C, N), largest cofactors proven prime by general methods (thank you David for them!), the most wanted factors to be factored/proven prime and so on. To avoid updating the big database, new results would be packed into a small "patch" database, updated monthly or about... An upper limit for N might be set to 2^33, because we have (1479*2^34+1)|Phi(2^33,2). Small factors (say, <2^24 for "general" numbers and <2^28*N when N is prime) need not to be kept, they are easy to found by trial division...

      A real idea or a dream?

      Thanks for comments,

      Andrey


      [Non-text portions of this message have been removed]
    • Andrey Kulsha
      ... And, of course, in Will Edgington s tables http://www.garlic.com/~wedgingt/mersdata.tgz . Best, Andrey [Non-text portions of this message have been
      Message 2 of 4 , Oct 13, 2002
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        > There are some information on Woltman's pages, Cunningham Project pages, Caldwell's Prime Pages, Lifchitz's PRP Top, our group archive, etc.

        And, of course, in Will Edgington's tables http://www.garlic.com/~wedgingt/mersdata.tgz .

        Best,

        Andrey


        [Non-text portions of this message have been removed]
      • Andrey Kulsha
        ... Just found a typo in them. It s written M( 32760 )C: 12878873281 there, but 12878873281=65521*196561, and PFGW reports gcd(phi(32760,2),12878873281) is
        Message 3 of 4 , Oct 13, 2002
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          > > There are some information on Woltman's pages, Cunningham Project pages, Caldwell's Prime Pages, Lifchitz's PRP Top, our group archive, etc.
          >
          > And, of course, in Will Edgington's tables http://www.garlic.com/~wedgingt/mersdata.tgz .


          Just found a typo in them. It's written

          "M( 32760 )C: 12878873281"

          there, but 12878873281=65521*196561, and PFGW reports

          gcd(phi(32760,2),12878873281) is Unity (1).

          Indeed, 65521|Phi(32760/28,2) and 196561|Phi(32760/3,2). Looks like somebody found 12878873281|(2^32760-1) by P-1 method and reported it as a factor of Phi(32760,2).

          Best,

          Andrey


          [Non-text portions of this message have been removed]
        • Will Edgington
          Just found a typo in them. It s written M( 32760 )C: 12878873281 there, but 12878873281=65521*196561, and PFGW reports gcd(phi(32760,2),12878873281) is Unity
          Message 4 of 4 , Oct 13, 2002
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            Just found a typo in them. It's written

            "M( 32760 )C: 12878873281"

            there, but 12878873281=65521*196561, and PFGW reports

            gcd(phi(32760,2),12878873281) is Unity (1).

            Indeed, 65521|Phi(32760/28,2) and 196561|Phi(32760/3,2). Looks like
            somebody found 12878873281|(2^32760-1) by P-1 method and reported
            it as a factor of Phi(32760,2).

            Yup, that's almost certainly the case. My update scripts will catch
            such composite or non-primitive factors eventually, but not always the
            first time; that would be quite expensive with all the data I am sent.
            I'll make sure this particular one is taken care of, but there are
            almost certainly others.

            Due to the details of my scripts, data for exponents above 30,000 will
            be less accurate in this sense, with that value slowly increasing over
            time as my computers get around to running SPRP tests of the current
            cofactors. My primary concern, however, is gaps in GIMPS and related
            trial factoring data due to bugs in prior versions of factoring
            programs, as I'm the only person that has such gaps data.

            Will

            http://www.garlic.com/~wedgingt/mersenne.html

            P.S. GIMPS, the Great Internet Mersenne Prime Search, is at
            http://www.mersenne.org/
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