Fermat prime

Definition with symbols
A natural number $$N$$ is said to be a Fermat prime if it satisfies the following equivalent conditions:


 * $$N$$ is prime and there exists a natural number $$n$$ such that $$N = 2^{2^n} + 1$$
 * $$N$$ is prime and there exists a natural number $$m$$ such that $$N = 2^m + 1$$
 * $$N$$ is prime and the automorphism group of the cyclic group of order $$N$$ is a 2-group

Stronger properties

 * Prime number

Weaker properties

 * Fermat prime product

Subject wiki links

 * Number theory wiki