Fermat number
Generalized Fermat numbers can be prime only for even , because if is odd then every generalized Fermat number will be divisible by 2. The smallest prime number formula_39 with formula_40 is formula_41, or 3032 + 1. Besides, we can define "half generalized Fermat numbers" for an odd base, a half generalized Fermat number to base "a" (for odd "a") is formula_42, and it is also to be expected that there will be only finitely many half generalized Fermat primes for each odd base.