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25591Re: Double Fermat+Frobenius

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  • djbroadhurst
    Aug 4, 2014
      Paul Underwood used up his monthly gremlin allowance
      with an 8-selfridge test that was very easy to fool:

      {ferfro(x,n)=gcd(x^3-x,n)==1&&kronecker(x^2-4,n)==-1&&
      Mod(2*x,n)^(n-1)==1&&Mod(Mod(1,n)*(L+x),L^2-x*L+1)^(n+1)==1+2*x^2;}

      {tst(n,x,y)=gcd(x^2-y^2,n)==1&&ferfro(x,n)&&ferfro(y,n);}

      {n=126256669511639877109;
      x=5031702531319296552;
      y=9025414833578502318;
      if(tst(n,x,y)&&!isprime(n),print(" Fooled this test."))};

       Fooled this test.

      David
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