fermat prime

Fermat prime

   <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)