One can fashion a LL test using same similar code of prime95 for Mersenne Numbers that for Fermat Numbers too! The Pepin's test exists for Fermat Numbers and is deterministic and polynomial. This new LL test for Fermats is also deterministic and polynomial in running time of Order O(2^2n) for Fn=2^2^n+1 and is polynomial in Computing Space as well unlike the Pepins test.
Thank you!
