Fermat number

Definition

Let $n$ be a nonnegative integer. The $n^{th}$ Fermat number, denoted $F_{n}$, is defined as:

$F_{n}:=2^{2^{n}}+1$.

If it is prime, it is termed a Fermat prime.

Relation with other properties

Weaker properties

• Proth number
• Generalized Fermat number

Other related properties

• Safe prime is a prime $p$ such that $(p-1)/2$ is also prime.
• Mersenne number is a number of the form $2^{n}-1$, and a Mersenne prime is a Mersenne number that is also prime.

Testing

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000215