 Fermat prime

A Fermat prime is a Fermat number that is also a prime number:The defining form alone does not imply primality. For example, $65537$ is a Fermat prime, while $4294967297$ is a Fermat number with proper divisors. For $k\ge 1$, every Fermat prime is one modulo four and two modulo three. Pépin's test gives an exact primality testing criterion for these candidates, rather than relying on their form.