Meaning of Fermat prime | Babel Free

Definitions

A Fermat number that is prime.

Examples

“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 every Fermat prime is a Fermat number, it is certainly not true that every Fermat number is prime.”

“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.”

“F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537. The next 28 Fermat numbers, F₅ through F₃₂, are known to be composite.”

CEFR level