Fermat prime

Noun

Fermat prime (plural Fermat primes)

1. A Fermat number that is prime.
   • It is not hard to prove that the only way that the number 1#43;2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1#43;2#123;2ᵃ#125; for integers a#92;ge 0. The numbers F#95;a#61;1#43;2#123;2ᵃ#125; are called Fermat numbers, and although it is true that...2001, I. Martin Isaacs, Geometry for College Students, American Mathematical Society, page 201
   • Rather surprisingly, it turns out that Fermat primes play an important special role in this context, a phenomenon hitherto unobserved in the arithmetic theory of Hecke groups, and, as a byproduct of our investigation, several new characterizations of Fermat primes are obtained.2004, T. W. Müller, “12: Parity patterns in Hecke groups and Fermat primes”, in Thomas Wolfgang Müller, editor, Groups: Topological, Combinatorial and Arithmetic Aspects, Cambridge University Press...