# Composite Fermat number

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## 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 .