919444^1048576+1 (new Generalized Fermat mega prime)

Mersenne prime: 2^n-1, for example 31=11111[base 2], we know 49 of them

Fermat prime: 2^(2^n)+1: for example 17=10001[base 2], we know 5 of them]

This is similar to a Fermat prime, but it's not exactly a Fermat prime. So the binary representation is horrible.

The main idea is that is you know the prime factorization of N+1 or N-1, then it's helpful to test if N is prime or not.