Loading ...
Sorry, an error occurred while loading the content.

Re: sufficient test for primes with certificate

Expand Messages
  • djbroadhurst
    ... Thanks, Bernhard, for acknowledging my disproof of your over-ambitious claim. I have found a counterexample with composite p 10^22. You might like to
    Message 1 of 33 , Jul 18, 2012
    • 0 Attachment
      --- In primenumbers@yahoogroups.com,
      "bhelmes_1" <bhelmes@...> wrote:

      > Dear David,
      > the counterexample is right and congratulation
      > to your efforts to find it so fast.

      Thanks, Bernhard, for acknowledging my disproof
      of your over-ambitious claim.

      I have found a counterexample with composite p > 10^22.
      You might like to check it:

      g = 7564150280291167283594;
      a = 895783764657097415398;
      p = 10006480882000194426451;

      {if(p%4 == 3 && !issquare(p) && !issquare(a) &&
      kronecker(a,p) == 1 && Mod(a,p)^((p-1)/2) == 1 &&
      Mod((1+x)*Mod(1,p),x^2-a)^((p-1)/2) == g*x &&
      Mod(g,p)^2*a == 1 && !isprime(p),
      print(" Counterexample with "#Str(p)" digits!"));}

      Counterexample with 23 digits!

      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
      • 0 Attachment
        --- 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
      Your message has been successfully submitted and would be delivered to recipients shortly.