--- 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

September.

David