Factoring numbers is a concept learnt with the introduction of divisibility in schools, yet the process can be exceptionally challenging and difficult. This category addresses topics from the basic divisibility tests to perfection and the general problem...
This page was last updated on October 9th, 2008
This page was last updated on October 9th, 2008
Factoring (from Number Theory)
Canadian Content » Science » Math » Number_Theory » Factoring »
Factoring Fermat Numbers
Cash prizes for new factors of Fermat numbers Fn, for n = 12 through 22.
FactorWorld
Dedicated to algorithms and computational results on integer factorization. Includes links to papers, downloadable software, and online resources.
Factoring Papers
Links to papers on the theory and practice of factoring.
Paul Herman's Factoring Page
A thorough summary of many major factoring methods. Includes some source code on many pages, gentle introductions to the more complex methods and further links.
I Love Binary, Primes, and Factors
Divisibility, primes and binary numbers.
The XYYXF Project
A collaborative project to produce the factorizations of x^y + y^x for 1<y<x<101.
Computing Aurifeuillian factors
Algorithm that finds non-trivial factors of certain numbers of the form a^b +/- 1.
Factoris
Online calculator that factorizes large numbers, specified by formula.
The Factor Zone
Aimed at grade school students and teachers, includes course guidelines, worksheets, and factor tables up to 600.
The Anti-Divisor
A definition and description of the Anti-Divisor, and some related results.
Sam Wagstaff
Article about SNFS factorisation of 3^349-1.
N!+-1 Factoring Status
Factoring efforts that have been made so far on numbers of the form n!+-1 using ECM factoring.
Sierpinski Problem
Sierpinski proved there exist infinitely many odd integers k such that k*2^n+1 is composite for every n. Ray Ballinger coordinates a search to prove or disprove whether k=78557 is the smallest solution.
RSA Laboratories Factoring Challenge
Numbers representative of those used in the RSA cryptosystem are offered for factor attempts with prizes. A Partition List challenge is also provided in order to encourage work on factoring in general.
Factorization Using the Elliptic Curve Method
Java applet that can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, the Euler's totient and moebius functions, and the decomposition of the number in a s
Known Amicable Pairs
A listing of all the known pairs of numbers, each of which is the sum of the aliquot divisors of the other. Complete for smaller numbers, and extending beyond 200 digits.
Factorization of RSA-155
Announcement of factorization of a 512-bit RSA key using the General Number Field Sieve (GNFS).
Number Field Sieve
Triade systems links to papers on the number field sieve.
Discovery of a Lost Factoring Machine
Built by a French amateur, E.-O. Carissan, around 1919. Shallit, Williams and Morain include photographs and references to their paper.
Robinson Primes
An analysis of problems relating to the numbers k.2^n+-1, primes, and factor patterns, including the Sierpinski problem.
Factorizations of Near-repdigit Numbers
Factorizations of numbers composed of all the same digit except first and/or last.
Factorization of F10
F10 = 2^(2^10) + 1 is the 10-th Fermat number. Richard Brent describes his discovery of the two largest factors.
Fermat Search
Leonid Durman's Fermat number factoring site and program.
Integer Factorization
Paul Leyland's list of his own and other factorisations.
Cash prizes for new factors of Fermat numbers Fn, for n = 12 through 22.
Dedicated to algorithms and computational results on integer factorization. Includes links to papers, downloadable software, and online resources.
Links to papers on the theory and practice of factoring.
A thorough summary of many major factoring methods. Includes some source code on many pages, gentle introductions to the more complex methods and further links.
Divisibility, primes and binary numbers.
A collaborative project to produce the factorizations of x^y + y^x for 1<y<x<101.
Algorithm that finds non-trivial factors of certain numbers of the form a^b +/- 1.
Online calculator that factorizes large numbers, specified by formula.
Aimed at grade school students and teachers, includes course guidelines, worksheets, and factor tables up to 600.
A definition and description of the Anti-Divisor, and some related results.
Article about SNFS factorisation of 3^349-1.
Factoring efforts that have been made so far on numbers of the form n!+-1 using ECM factoring.
Sierpinski proved there exist infinitely many odd integers k such that k*2^n+1 is composite for every n. Ray Ballinger coordinates a search to prove or disprove whether k=78557 is the smallest solution.
Numbers representative of those used in the RSA cryptosystem are offered for factor attempts with prizes. A Partition List challenge is also provided in order to encourage work on factoring in general.
Java applet that can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, the Euler's totient and moebius functions, and the decomposition of the number in a s
A listing of all the known pairs of numbers, each of which is the sum of the aliquot divisors of the other. Complete for smaller numbers, and extending beyond 200 digits.
Announcement of factorization of a 512-bit RSA key using the General Number Field Sieve (GNFS).
Triade systems links to papers on the number field sieve.
Built by a French amateur, E.-O. Carissan, around 1919. Shallit, Williams and Morain include photographs and references to their paper.
An analysis of problems relating to the numbers k.2^n+-1, primes, and factor patterns, including the Sierpinski problem.
Factorizations of numbers composed of all the same digit except first and/or last.
F10 = 2^(2^10) + 1 is the 10-th Fermat number. Richard Brent describes his discovery of the two largest factors.
Leonid Durman's Fermat number factoring site and program.
Paul Leyland's list of his own and other factorisations.
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