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25543Re: Quad Frobenius test

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  • djbroadhurst
    May 10, 2014
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      Paul Underwood proposed a 12-selfridge test:


      This seems gremlin-proof. The gremlins can easily find triples
      [c,x,n] with dblfro(c,x,n)=1 and kronecker(x^2-4)=-1, for
      semiprime n=p*q. But the construction yields only 4 values of c
      for a given pair [x,n], since c^2 is determined by x^2, modulo p
      and modulo q. It follows that if [a,b] are two of the 4 possible
      values of c, then gcd(a^2-b^2,n)>1, by construction.

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