Fermat prime

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(mathematics)

Fermat prime - 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.

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No references found			Subsequently Gauss presented this result at the end of Disquistiones Arithmeticae, in which he proves the constructibility of the n-gon for any n that is a prime of the form [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] also known as Fermat primes. Carl Friedrich Gauss by Rice, Kathryn; Scott, Paul / Australian Mathematics Teacher Almost all number theorists consider the first Fermat prime to be [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], so that the first five Fermat numbers are prime. Letters by Science News			ferghanite Fergus Fergus County Fergus Falls Ferguson Ferguson, Adam Ferguson, b. Ferguson, George Ferguson, Homer Ferguson, James Edward Ferguson, Maynard Ferguson, Miriam A. Wallace Ferguson, Patrick Ferguson, Samuel Ferguson, Sir Samuel fergusonite Fergusson, Robert Ferhat Abbas Feriaz Ferishta Ferlinghetti Ferlinghetti, Lawrence Fermanagh Fermat Fermat numbers Fermat prime Fermat's Last Theorem Fermat's Principle Fermat's spiral Fermat's Theorem Fermat, Pierre de ferme ornee ferme ornée ferment ferment oil Fermentation fermentation accelerator Fermentation of Fodder fermentation tube fermented milk fermenter Fermenting Vat Fermentnaia I Spirtovaia Promyshlennost Ferments fermi Fermi age Fermi age equation Fermi age model Fermi beta-decay theory Fermi constant Fermi derivative			Fermaldehyde Fermaldihyde Fermaldihyde Fermaldihyde Fermaldihyde Ferman Fermanagh Fermanagh Fermanagh Fermanagh Lakeland School of English Fermanagh Rural Community Initiative Fermanagh Voluntary Association of the Disabled Fermanagh, Armagh, Tyrone, Londonderry, Antrim, Down Fermanted beverage Fermanted beverage Fermanted beverage FERMAR Fermat Fermat Fermat Fermat conjecture Fermat conjecture Fermat great theorem Fermat great theorem Fermat last theorem Fermat last theorem Fermat number Fermat numbers Fermat Numbertransform Fermat Pierre de Fermat prime Fermat principle Fermat principle Fermat pseudoprime Fermat spiral Fermat theorem Fermat's conjecture Fermat's conjecture Fermat's equation Fermat's great theorem Fermat's great theorem Fermat's last theorem Fermat's last theorem Fermat's last theorem Fermat's Last Theorem Applies Fermat's little theorem Fermat's principle Fermat's principle Fermat's spiral Fermat's theorem Fermat, Pierre de Fermat, Pierre de Fermat-Euler theorem Fermat-Wiles Theorem Fermat-Wiles Theorem fermata Fermata Over Whole Rest fermatas Fermats Last Theorem Fermats Last Theorem Fermats principle

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