Fermat prime

This article defines a property that can be evaluated for natural numbers

Definition

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

Relation with other properties

Stronger properties

• Prime number

Weaker properties

• Fermat prime product