Fermat number
Positive integer of the form (2^(2^n))+1 / From Wikipedia, the free encyclopedia
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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: 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).
Quick Facts Named after, No. of known terms ...
Named after | Pierre de Fermat |
---|---|
No. of known terms | 5 |
Conjectured no. of terms | 5 |
Subsequence of | Fermat numbers |
First terms | 3, 5, 17, 257, 65537 |
Largest known term | 65537 |
OEIS index | A019434 |
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If 2k + 1 is prime and k > 0, then k itself must be a power of 2,[1] so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023[update], the only known Fermat primes are F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence A019434 in the OEIS).