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 $n$.