# Composite Fermat number

From Number

## Contents

## Definition

A **composite Fermat number** is a Fermat number that is also a composite number, i.e., it is not a Fermat prime.

## Facts

### Constraints on prime divisors

`Further information: Prime divisor of Fermat number is congruent to one modulo large power of two`

If , and is a composite Fermat number, then divides for any prime divisor of . As a corollary, divides for *any* divisor of .

## Relation with other properties

### Weaker properties

- Composite Proth number
- Poulet number: It is a Fermat pseudoprime to the base .
- Strong pseudoprime to base .