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In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
where n is a non-negative integer. The first few Fermat numbers are:
If 2k + 1 is prime and k > 0, then k must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023, the only known Fermat primes are F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence A019434 in the OEIS); heuristics suggest that there are no more.