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Re: sufficient test for primes with certificate

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  • djbroadhurst
    In primenumbers@yahoogroups.com, ... No. ... Your attempted proof wrongly assumes that a positive kronecker implies ... Let P = 15. ... Let A = 2. Then your
    Message 1 of 33 , Jul 14, 2012
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      In primenumbers@yahoogroups.com,
      "bhelmes_1" <bhelmes@...> asked:

      > Is the mathematical proof right

      No.

      Your test uses the kronecker symbol:

      > a is a number with jacobi (a,p)=1

      Your attempted "proof" wrongly assumes
      that a positive kronecker implies
      a quadratic residue:

      > Now, let P be composite = p1^k1 * p2^k2 * ....

      Let P = 15.

      > Let A be a square residue mod P.

      Let A = 2. Then your test would record that

      kronecker(2,15) = 1

      > there exist x such that x^2 = A mod P.

      False. There is no x such that x^2 = 2 mod 15.
      Moreover, you have been told this before.

      David
    • paulunderwooduk
      ... I compiled a better version of my code with gmp 5.0.5, on a different box running at 3.6GHz and got some better timings { 17.505s pfgw (3-prp) 1m1.986s
      Message 33 of 33 , Sep 21, 2012
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        --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:
        :
        > http://tech.groups.yahoo.com/group/primenumbers/files/Articles/

        > I ran various "minimal \lambda+2" tests on Gilbert Mozzo's 20,000 digit PRP, 5890*10^19996+2^66422-3 (x=1), using a 2.4GHz core:
        > {
        > 0m32.374s pfgw64 (3-prp)
        > 1m9.876s pfgw64 -t
        > 1m53.535s pfgw64 -tp
        > 3m0.483s pfgw64 -tc
        > 5m12.972s pfgw64 scriptify
        > 4m4.811s gmp (-O3/no pgo)
        > 4m9.148 pari-gp
        > 1m15s theoretical Woltman implementation
        > }
        >

        I compiled a better version of my code with gmp 5.0.5, on a different box running at 3.6GHz and got some better timings
        {
        17.505s pfgw (3-prp)
        1m1.986s pfgw -tp
        1m13.789s gmp (-O3/no pgo)
        }

        Paul
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