- --- In primenumbers@yahoogroups.com,

"bhelmes_1" <bhelmes@...> wrote:

> let be b the smallest non quadric residium.

This looks to be hard to fool, since it is very similar to BPSW.

> Necessary: b^((p-1)/2)=p-1 mod p

> Sufficent: (b+I)^p = b^p + I^p = b - I

However it is wilful nonsense to claim that such a test

proves primality. Please replace "suffic[i]ent" by "necessary".

David - --- In primenumbers@yahoogroups.com,

"bhelmes_1" <bhelmes@...> wrote:

> there might be counterexamples if you do not take the smallest b

It's very easy to fool your test, in that case:

{tst(n,b)=n%4==3&&kronecker(b,n)==-1&&

Mod(b,n)^((n-1)/2)==-1&&

Mod(Mod(1,n)*(b+x),x^2+1)^n==b-x;}

if(tst(337*3079,298117),print(fooled));

fooled

David - --- In primenumbers@yahoogroups.com,

"bhelmes_1" <bhelmes@...> wrote:

> The good news is that the test "only" need 3 Selfridges

Wrong again. You are still using 1+3=4 selfridges.

Please see Theorem 3.5.8 of Crandall and Pomerance.

David