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A prime factorization algorithm is any algorithm by which an integer (whole number) is "decomposed" into a product of factors that are prime numbers (see prime factor). The fundamental theorem of arithmetic guarantees that this decomposition is unique. This article gives a simple example of an algorithm, which works well for numbers whose prime factors are small; faster algorithms for numbers with larger prime factors are discussed in the article on integer factorization. A 'fast' algorithm (which can factorise large numbers in a reasonably small time) is much sought after.
A simple factorization algorithm
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Tables :: Number Theory
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Brilliant Numbers - Tables of maximal and minimal numbers with two, three or four prime factors of the same length (in decimal notation).
Meta Description: [ Interesting problem about products of two primes of the same size. ]
Cunningham Project - Current status of the project to factor numbers of the form b^n +/- 1, b = 2, 3, 5, 6, 7, 10, 11, and 12. Maintained by Samuel S. Wagstaff, jr.
Factor Tables - Richard Brent's tables extend the scope of the Cunningham project (factoring b^n+-1) to all applicable bases b less than 100, plus some higher bases.
Factorization of Cyclotomic Numbers - Hisanori Mishima is coordinating the search and producing tables of factorizations of cyclotomic numbers for values of phi(n) less than 48.
Factorization Results - Tables, summaries, and links to many factoring endeavors, including primorials, factorials, and cyclotomic polynomials. Includes theorems and descriptions behind each project.
Factorizations of Repunit Numbers - Tables available in text and compressed format.
Factors - Lists the factors of every single number up to 600, for quick reference and as a resource for students.
Factors of 2^n + or - 1 - Factorizations for values of n up to 10000, extending the results of the Cunningham Project.
Factors of Modified Fermat Numbers - Factors of numbers of the form 4^(3^n)+2^(3^n)+1 and 4^(3^n)-2^(3^n)+1.
Meta Description: [ Factors of numbers of the form 4^(3^n)+2^(3^n)+1 and 4^(3^n)-2^(3^n)+1. ]
Factors of Numbers near Googolplex - This table includes all known prime factors of the numbers in the range 10^(10^100) to 10^(10^100)+999, including more than 57000 prime factors of googolplex + 10.
Meta Description: [ Factors of numbers in the range 10^(10^100) to 10^(10^100)+999. ]
Fermat Factoring Status - Compiled by Wilfrid Keller, lists the known prime factors and complete factorizations of Fermat numbers.
Fibonacci and Lucas Factorizations - Tables of known factorizations of the first 10,000 Fibonacci and Lucas numbers.
Prime Factorization of Cyclotomic Numbers - Factor tables of cyclotomic numbers for values of phi(n) up to 120 by Mitsuo Morimoto.
Repunit Primes and Factors - Factors of 10^n +- 1 for n1000.
| . This, the Fletcher Capstan Table, is the only table in the world with its unique properties. It is a circular table ... | |
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