24809Re: mod quartic composite tests
- Jan 9, 2013--- In firstname.lastname@example.org, "paulunderwooduk" wrote:
>n=287051 and x=3988 is a counterexample.
> I have devised a new composite test for odd n with x:
> gcd(x^3-x,n)==1 (mod n)
> and the sub-test:
> (L+1)^n==-L^3+(x^2-2)*L+1 (mod n, (L^2-x*L+1)*(L^2+x*L+1))
> Can you find a counterexample?
> If this is too easy for you, please try:This test is (1)+(1)+(2)+(2)+9 selfridge for small x, where (1) is a fermat test and (2) is a frobenius test over L^2-x*L+1 or L^2+x*L+1.
> (L+2)^n==-L^3+(x^2-2)*L+2 (mod n, (L^2-x*L+1)*(L^2+x*L+1))
I already have:
"Non-square N>1 is prime if and only if for any integer x such that
then both (L+-2)^(N+1)==5+-2*x (mod N, L^2-x*L+1) (Both L+-2 needed.)
Verified for odd N< 10^7."
- << Previous post in topic Next post in topic >>