Definition:Fermat Prime

Definition
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.

No Fermat prime for $n > 4$ has ever been discovered.

Also see

 * Primes of form Power of Two plus One
 * Are there any more Fermat Primes?
 * Fermat Prime Conjecture