There are two different definitions of generalized Fermat numbers, one of which is more general than the other. Ribenboim (1996, pp. 89 and 359-360) defines a generalized Fermat number as a number of the form a^(2^n) + 1 with a>2, while Riesel further generalizes, defining it to be a number of the form a^(2^n) + b^(2^n). Both definitions generalize the usual Fermat numbers F_n = 2^(2^n) + 1. The following table gives the first few generalized Fermat numbers for various bases a.

Fermat number | Fermat prime | near-square prime

Pierre de Fermat