Factoring
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.
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'…
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.
Generalised Mersenne Numbers
Numbers of the form b^n +- (b-1), factorised by Wojciech Florek.
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.
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 …
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