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'Lucas-Lehmer primality test'
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| Title of object: |
Lucas-Lehmer primality test |
| Canonical Name: |
LucasLhemer |
| Type: |
Theorem |
| Created on: |
2004-06-11 07:55:04 |
| Modified on: |
2004-11-26 07:09:54 |
| Classification: |
msc:11A51 |
Revision comment (for changes between this and next version):
| Changes for correction #13471 ('Very minor details'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
\textbf{Theorem:} Let $p>2$ be a prime, and let $M_p$ be a
Mersenne number, then $M_p$ is prime iff $M_p$ divides $s_{p-1}$
where the numbers $(s)_{n\geq1}$ are given by the following
relation: $s_1=4$, $s_{n+1}=s_n^2-2$ for $n\geq1$. |
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