# Difference between revisions of "Pierre de Fermat"

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The first eight Fermat numbers are | The first eight Fermat numbers are | ||

− | * F<sub> | + | * F<sub>0</sub> = 2<sup>1</sup> + 1 = 3 |

− | * F<sub> | + | * F<sub>1</sub>= 2<sup>2</sup> + 1 = 5 |

− | * F<sub> | + | * F<sub>2</sub>= 2<sup>4</sup> + 1 = 17 |

− | * F<sub> | + | * F<sub>3</sub> = 2<sup>8</sup> + 1 = 257 |

− | * F<sub> | + | * F<sub>4</sub> = 2<sup>16</sup> + 1 = 65537 |

As of 2007, only the first 12 Fermat numbers have been completely factored see: http://www.prothsearch.net/fermat.html. | As of 2007, only the first 12 Fermat numbers have been completely factored see: http://www.prothsearch.net/fermat.html. |

## Revision as of 15:46, 14 May 2007

Frenchman **Pierre de Fermat** (1601–1665) was one of the two leading mathematicians of the early 1600s, the other being Rene Descartes. Fermat was a founder of the modern theory of numbers, discovered the fundamental principle of analytic geometry (independent of Descartes' work) and helped found the theory of probability (with Blaise Pascal). By trade Fermat was a lawyer.

Fermat's most famous equation is Fermat's Last Theorem, which was not proven until American mathematician Andrew Wiles published his proof in 1993. Wiles was born an Englishman, but was awarded US citzenship for solving Fermat's equation.

A Fermat number is a positive integer of the form

F_{n} = 2^{2n} + 1

where n is a nonnegative integer.

The first eight Fermat numbers are

- F
_{0}= 2^{1}+ 1 = 3 - F
_{1}= 2^{2}+ 1 = 5 - F
_{2}= 2^{4}+ 1 = 17 - F
_{3}= 2^{8}+ 1 = 257 - F
_{4}= 2^{16}+ 1 = 65537

As of 2007, only the first 12 Fermat numbers have been completely factored see: http://www.prothsearch.net/fermat.html.