Fermat prime

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.
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Definition

A Fermat prime is a Fermat number that is also a prime number. In other words, it is a prime number of the form $F_k=2^{2^k}+1$, where $k$ is a nonnegative integer.

It turns out that if $2^n+1$ is prime for $n$ a natural number, then $n=2^k$ for some nonnegative integer $k$. Thus, a Fermat prime can also be defined as a prime of the form $2^n+1$ for some natural number $n$.

Relation with other properties

Weaker properties

• Proth prime

Testing

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A019434