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25333Re: Two parameter PRP test

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  • djbroadhurst
    Aug 4, 2013
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      --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:

      > am I cheating?

      > {tst(n,x,k)=gcd(x*k,n)==1&&
      > kronecker((x+3*k)*(x-k),n)==-1&&
      > kronecker((x-3*k)*(x+k),n)==-1&&
      > Mod(x*k-k^2,n)^(n-1)==1&&
      > Mod(x*k+k^2,n)^(n-1)==1&&
      > Mod(Mod(1,n)*L,L^2-(x+k)/k*L+1)^(n+1)==1&&
      > Mod(Mod(1,n)*L,L^2-(x-k)/k*L+1)^(n+1)==1;}

      That seems like a fair 6-Selfridge double-Lucas test
      with two free parameters. So it ought to be foolable
      by choosing a pair of appropriate cosines.

      However, you have used up your monthly credit,
      so expect counterexamples from the Gremlins in

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