fermat prime

Computing Dictionary

Fermat prime definition

mathematics
A prime number of the form 2^2^n + 1. Any prime number of the form 2^n+1 must be a Fermat prime. Fermat conjectured in a letter to someone or other that all numbers 2^2^n+1 are prime, having noticed that this is true for n=0,1,2,3,4.
Euler proved that 641 is a factor of 2^2^5+1. Of course nowadays we would just ask a computer, but at the time it was an impressive achievement (and his proof is very elegant).
No further Fermat primes are known; several have been factorised, and several more have been proved composite without finding explicit factorisations.
Gauss proved that a regular N-sided polygon can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct Fermat primes.
(1995-04-10)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
Cite This Source
Explore Dictionary.com
Previous Definition: fermat last theorem
Next Definition: fermat principle
Words Near: fermat prime
More from Thesaurus.com
Synonyms and Antonyms for fermat prime
More from Reference.com
Search for articles containing fermat prime
More from Dictionary.com Translator
Dictionary.com Word FAQs

Dictionary.com presents 366 FAQs, incorporating some of the frequently asked questions from the past with newer queries.

Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature