Fermat number
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 , where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, .... If 2k + 1 is prime and k > 0, then k itself 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.
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