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Computing (FOLDOC) dictionary
Fermat prime
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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.