\begin{definition}[Definition:Fermat Prime]
A '''Fermat prime''' is a Fermat number, that is a number of the form $2^{\paren {2^n} } + 1$, which happens to be prime.
In fact, $2^{\paren {2^n} } + 1$ is prime for $n = 0, 1, 2, 3, 4$.
However, $2^{\paren {2^5} } + 1 = 2^{32} + 1$ is divisible by $641$, as was proved by {{AuthorRef|Leonhard Paul Euler|Euler}}.
No '''Fermat prime''' for $n > 4$ has ever been discovered.
\end{definition}