Dictionary

Fermat prime en · NOUN

Etymology

Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665).

Meanings

1. A Fermat number that is prime.
   • F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537. The next 28 Fermat numbers, F₅ through F₃₂, are known to be composite. 2013, Dean Hathout, Wearing Gauss’s Jersey, Taylor & Francis (CRC Press), page xi, Believe it or not, so far only five Fermat primes are known
   • 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. 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, page 327:

Forms

Coordinates

Sophie Germain prime · Mersenne prime

Relateds

Fermat number

Translations (1)

bg про́сто число́ на Ферма́ (Fermat number that is prime)