<mathematics> 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.
(1995-04-10)
Try this search on Wikipedia, OneLook, Google
Nearby terms: fencepost error « fepped out « FEPROM « Fermat prime » Fermat's Last Post » Ferranti F100-L » ferrite core memory
<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].
(2012-02-19)
Try this search on Wikipedia, OneLook, Google
Nearby terms: fepped out « FEPROM « Fermat prime « Fermat's Last Post » Ferranti F100-L » ferrite core memory » Ferroelectric RAM
