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25588Double Fermat+Frobenius

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  • paulunderwooduk
    Aug 2, 2014
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      Where the kronecker and gcd conditions are met, here is a 8 selfridge test for n coprime to 30:

      {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);}

      I have verified this for n < 10^7. Can you find a pseudoprime for this test?

      Paul
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