Fermat prime

English

Etymology

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

Noun

Fermat prime (plural Fermat primes)

  1. (number theory) A Fermat number that is prime.
    Coordinate terms: Mersenne prime, Sophie Germain prime
    • 2001, I. Martin Isaacs, Geometry for College Students, American Mathematical Society, page 201:
      It is not hard to prove that the only way that the number can possibly be prime is when is a power of 2, and so all Fermat primes must have the form for integers . The numbers 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.
    • 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:
      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.
    • 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:
      F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537.
      The next 28 Fermat numbers, F5 through F32, are known to be composite.

Further reading

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