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Fermat Primes
Basic Info
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

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