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25571Re: Quad Frobenius test

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  • djbroadhurst
    Jul 2, 2014
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      Paul Underwood wrote:

      > I have generalized the test

      Here, at some cost, is a pseudoprime:

      {gsgl(c,a,P,Q,n)=Mod(Mod(1,n)*(c*L+a),L^2-P*L+Q)^(n+1)==(c*P+a)*a+c^2*Q;}

      {gdbl(c,a,P,Q,n)=gsgl(c,a,P,Q,n)&&gsgl(c,-a,P,Q,n);}

      {gtst(c,a,b,P,Q,n)=a!=b&&gcd(c*a*b*P*Q,n)==1&&
      gcd(a^2-b^2,n)==1&&kronecker(P^2-4*Q,n)==-1&&
      gdbl(c,a,P,Q,n)&&gdbl(c,b,P,Q,n);}

      {c=1;
      n=825788694491;
      a=204485535519;
      b=199308455496;
      P=706289558640;
      Q=476711813288;
      if(gtst(c,a,b,P,Q,n)&&!isprime(n),
      print(" Found a pseudoprime."));}

       Found a pseudoprime.

      PS: The Gremlins will entertain no wriggle
      and decline further searching for a month or so.

      David



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