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In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form: F n = 2 2 n + 1, {\displaystyle F_{n}=2^{2^{n}}+1,} where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617,... (sequence A000215 in the OEIS).

If 2 + 1 is prime and k > 0, then k itself must be a power of 2, so 2 + 1 is a Fermat number; such primes are called Fermat primes. As of 2023, the only known Fermat primes are F = 3, F = 5, F = 17, F = 257, and F = 65537 (sequence A019434 in the OEIS).