Definition:Fermat Number
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Definition
A Fermat number is a natural number of the form $2^{\left({2^n}\right)} + 1$, where $n = 0, 1, 2, \ldots$.
The number $2^{\left({2^n}\right)} + 1$ is, in this context, often denoted $F_n$.
The first few Fermat numbers are:
- $3, 5, 17, 257, 65537, 4294967297, \ldots$
This sequence is A000215 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Also see
Source of Name
This entry was named for Pierre de Fermat.
He conjectured (incorrectly) that all numbers of this form are prime.
