Fn=3, 5, 17, 257, 65537, ...
Only these 5 Fermat primes are known, and it is unknown if there are others.
The Fermat primes are related to construction with compass and straightedge of a regular polygon with N sides.
To say more, a regular polygon with N sides can be constructed with compass and straightedge if and only if
the number of sides is
2a p1p2p3...pn with the pi are different Fermat primes (a Gauss theorem).
Then polygons with 3,4,5,6,8,10,12,15,16,17,20... sides can be constructed
Polygons with 7,9,11,13,14,18,19... sides can't be constructed.
3×5×17×257×65537 = 232 - 1
strange, isn't it ? ...