Fermat prime

English Fermat number Etymology en Pierre de Fermat 1601 1665 French lawyer and amateur mathematician =. Pronunciation en aɪm 3 Noun en number theory A Fermat number that is prime. en Mersenne prime Sophie Germain prime en 2001 I. Martin Isaacs Geometry for College Students w:American Mathematical Society https://books.google.com.au/books?id=0ahK8UneO3kC&pg=PA201&dq=%22Fermat+prime%22%7C%22Fermat+primes%22&hl=en&sa=X&ved=0ahUKEwiMt9mL-9rcAhXBFjQIHQotC9oQ6AEIKzAB#v=onepage&q=%22Fermat%20prime%22%7C%22Fermat%20primes%22&f=false 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. en 2004 T. W. Müller 12: Parity patterns in Hecke groups and Fermat primes Thomas Wolfgang Müller Groups: Topological, Combinatorial and Arithmetic Aspects w:Cambridge University Press https://books.google.com.au/books?id=w0QhgFBSXJYC&pg=PA327&dq=%22Fermat+prime%22%7C%22Fermat+primes%22&hl=en&sa=X&ved=0ahUKEwiMt9mL-9rcAhXBFjQIHQotC9oQ6AEIdjAP#v=onepage&q=%22Fermat%20prime%22%7C%22Fermat%20primes%22&f=false 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. Related terms en Fermat number Translations Fermat number that is prime Bulgarian: bg про́сто число́ на Ферма́ n Further reading Fermat Number on MathWorld Wolfram MathWorld