Source : Free On-Line Dictionary of Computing

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.
     
        (1995-04-10)