Definition:Fermat Number

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 $$F_n$$.

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

See Fermat Prime.