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'probable prime'
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| Title of object: |
probable prime |
| Canonical Name: |
ProbablePrime |
| Type: |
Definition |
| Created on: |
2006-05-04 17:00:31 |
| Modified on: |
2006-05-04 17:00:31 |
| Classification: |
msc:11A41 |
Revision comment (for changes between this and next version):
| Linked pseudoprime to PseudoprimeP |
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
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Content:
A sufficiently large odd integer $q$ believed to be a prime number because it has passed some preliminary primality test relative to a given base, or a pattern suggests it might be prime, but it has not yet been subjected to a conclusive primality test.
For primes with no specific form, it is required to test every potential prime factor $p < \sqrt{q}$ to be absolutely sure that $q$ is in fact a prime. For Mersenne probable primes, the Lucas-Lehmer test is accepted as a conclusive primality test.
Once a probable prime is conclusively shown to be a prime, it of course loses the label "probable." It also loses it if conclusively shown to be composite, but in that case it might then be called a pseudoprime relative to base $a$.
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