where n is a natural number. There are only five known Fermat primes: 3 (n=0), 5 (n=1), 17 (n=2), 257 (n=3) and 65537 (n=4). It is not known whether these are the only Fermat primes, and it is not even known whether or not there are infinitely many Fermat primes.
Carl Friedrich Gauss proved that there is a relationship between the ruler and compass construction of regular polygons and Fermat primes: a regular ngon can be constructed with ruler and compasses if and only if n is a power of 2 or the product of a power of 2 and distinct Fermat primes.
Integers of the general form
Different Fermat numbers are relatively prime.
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