Division Rules
Digital Divisibility Tests, Divisibility Criteria, Divisibility Tests, Divisibility Tests, Divisibility Tests, Divisibility War, Explaining the Divisibility Rules, The Anti-Divisor
Perfect Numbers
Aliquot, Aliquot Sequences, Aliquot Sequences, Aliquot Sequences, Aliquot Sequences, Amicable Numbers, Cubes of Perfection, Multiply Perfect Numbers, Odd Perfect Numbers - Missing Values, On a Generalization of Perfect Numbers
Tables
Brilliant Numbers, Cunningham Project, Factor Tables, Factorization of Cyclotomic Numbers, Factorization Results, Factorizations of Repunit Numbers, Factors, Factors of 2^n + or - 1, Factors of Modified Fermat Numbers, Factors of Numbers near Googolplex
Computing Aurifeuillian factors
Algorithm that finds non-trivial factors of certain numbers of the form a^b +/- 1.
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.
Factoring Fermat Numbers
Cash prizes for new factors of Fermat numbers Fn, for n = 12 through 22.
Factoring Papers
Links to papers on the theory and practice of factoring.
Factoris
Online calculator that factorizes large numbers, specified by formula.
Factorization of F10
F10 = 2^(2^10) + 1 is the 10-th Fermat number. Richard Brent describes his discovery of the two largest factors.
Factorization of RSA-155
Announcement of factorization of a 512-bit RSA key using the General Number Field Sieve (GNFS).
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 sum of up to four squares.
Factorizations of Near-repdigit Numbers
Factorizations of numbers composed of all the same digit except first and/or last.
FactorWorld
Dedicated to algorithms and computational results on integer factorization. Includes links to papers, downloadable software, and online resources.
I Love Binary, Primes, and Factors
Divisibility, primes and binary numbers.
Integer Factorization
Paul Leyland's list of his own and other factorisations.
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.
N!+-1 Factoring Status
Factoring efforts that have been made so far on numbers of the form n!+-1 using ECM factoring.
Number Field Sieve
Triade systems links to papers on the number field sieve.
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.
Robinson Primes
An analysis of problems relating to the numbers k.2^n+-1, primes, and factor patterns, including the Sierpinski problem.
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.
Sam Wagstaff
Article about SNFS factorisation of 3^349-1.
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.
The Anti-Divisor
A definition and description of the Anti-Divisor, and some related results.
The Factor Zone
Aimed at grade school students and teachers, includes course guidelines, worksheets, and factor tables up to 600.
The XYYXF Project
A collaborative project to produce the factorizations of x^y + y^x for 1<y<x<101.