--- In

primenumbers@yahoogroups.com,

"j_chrtn" <j_chrtn@...> wrote:

> Do you know if this test is something well known?

It's not well known because it's quite unnecessary.

The foolproof "unified Sophie" test that works in

*all* cases is much simpler.

If p is prime, then q = 2*p+1 is prime iff 4^p = 1 mod q.

Proof: Simply use base 2 in Pocklington's theorem and

observe that 2^2-1 is coprime to 2*p+1 for every prime p.

Note that this test detects *every* Sophie pair,

including [2,5] and [3,7]. Here is a sanity check:

Pock(p)=Mod(4,2*p+1)^p==1;

forprime(p=2,10^6,if(Pock(p)!=isprime(2*p+1),print(fail)));

\\ The rest is silence, signifying consent

Entia non sunt multiplicanda praeter necessitatem :-)

http://en.wikisource.org/wiki/The_Myth_of_Occam's_Razor
David [second attempt at a reply; apologies if it appears twice]