## Fermat prime

A prime number of the form 2^2^n + 1. Any prime number of the form 2^n+1 must be a Fermat prime. Fermat conjectured in a letter to someone or other that all numbers 2^2^n+1 are prime, having noticed that this is true for n=0,1,2,3,4.

Euler proved that 641 is a factor of 2^2^5+1. Of course nowadays we would just ask a computer, but at the time it was an impressive achievement (and his proof is very elegant).

No further Fermat primes are known; several have been factorised, and several more have been proved composite without finding explicit factorisations.

Gauss proved that a regular N-sided polygon can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct Fermat primes.

Last updated: 1995-04-10

## Fermat's Last Post

<humour>

A post to a bug tracker, mailing list or forum in which the author claims to have found a simple fix or workaround for a bug, but never says what it is and never shows up again to explain it (even after others have been puzzling over the bug for years).

[Dodgy Coder].

Last updated: 2012-02-19

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