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A Fermat prime is a prime of the form .

The only known Fermat primes are 3, 5, 15, 195 and 31E15, for n = 1, 2, 3, 4 and 5. It is conjectured that these five terms are the only Fermat primes. It can be proven that can only be prime if n is a power of 2.

Primality of Fermat numbers[]

The smallest composite Fermat number is 9EX461595, with prime factorization 455 × 22E1681.