There are two definitions of the Fermat number. The less common is a number of the form 2^n + 1 obtained by setting x = 1 in a Fermat polynomial, the first few of which are 3, 5, 9, 17, 33, ... (OEIS A000051). The much more commonly encountered Fermat numbers are a special case, given by the binomial number of the form F_n = 2^(2^n) + 1. The first few for n = 0, 1, 2, ... are 3, 5, 17, 257, 65537, 4294967297, ... (OEIS A000215).

Cullen number | Fermat polynomial | Fermat prime | generalized Fermat number | near-square prime | Pépin's test | Pépin's theorem | Pocklington's theorem | polygon | Proth prime | Proth's theorem | Selfridge-Hurwitz residue | Woodall number