Definition:Fermat Number

Definition
A Fermat number is a natural number of the form $2^{\left({2^n}\right)} + 1$, where $n = 0, 1, 2, \ldots$.

The number $2^{\left({2^n}\right)} + 1$ is, in this context, often denoted $F_n$.

The first few Fermat numbers are:
 * $3, 5, 17, 257, 65537, 4294967297, \ldots$

Also see

 * Fermat Prime.

He conjectured (incorrectly) that all numbers of this form are prime.