|Discovered by||Pierre de Fermat|
|Number of||Exactly five- Fermat numbers apart from the first five are composite|
|Description||A prime which is one more than two to the power of a power of two|
|First Few||3, 5, 17, 257, 65,537|
Fermat primes are Fermat numbers that are also prime numbers. A Fermat number has the following properties: Fn = 2(2^n) + 1.
All the Fermat primes
Note that 65,537 (F5) is the largest known Fermat prime, being 216 + 1. The next Fermat number (F6), 232 + 1 = 4,294,967,297, is divisible by 641 and 6,700,471.
Applications in Mathematics
Fermat primes are related to constructible polygons- regular polygons which one can construct using only a straightedge and circles. Polygons can be constructed if the number of sides' prime factors are either powers of two or powers of Fermat primes