The Fermat primes are the Fermat numbers that are prime.

**Pierre Fermat** conjectured in the sixteenth century that any number like this:

where Fn are the **Fermat numbers**, are **prime** numbers for any **natural n**.

It was not until **1730** when the mathematician **Leonhard Euler** proved that for **n = 5** the number was **divisible** by 641.

Thus proving Fermat’s conjecture was **false**.

Despite this, Fermat numbers have some **properties** studied that relate to prime numbers and hence still further research to learn **how many** Fermat primes are there and if those are **finite**.