| Directory > Science > Math > Number Theory > Factoring Computing Aurifeuillian factors
Algorithm that finds non-trivial factors of certain numbers of the form a^b +/- 1.
http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub127.html
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Factorizations of Near-repdigit Numbers
Factorizations of numbers composed of all the same digit except first and/or last.
http://homepage2.nifty.com/m_kamada/math/factorizations.htm
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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.
http://amicable.homepage.dk/knwnap.htm
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Factoring Fermat Numbers
Cash prizes for new factors of Fermat numbers Fn, for n = 12 through 22.
http://www.perfsci.com/prizes.html
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Factoring Papers
Links to papers on the theory and practice of factoring.
http://www.crypto-world.com/FactorPapers.html
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Paul Herman's Factoring Page
Theory, source code, further links.
http://www.frenchfries.net/paul/factoring/
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Number Field Sieve
Triade systems links to papers on the number field sieve.
http://triade.studentenweb.org/Nfs/nfs.html
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The XYYXF Project
A collaborative project to produce the factorizations of x^y + y^x for 1<y<x<101.
http://xyyxf.at.tut.by/
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Factorization of RSA-155
Announcement of factorization of a 512-bit RSA key using the General Number Field Sieve (GNFS).
http://www.crypto-world.com/announcements/RSA155.txt
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FactorWorld
Dedicated to algorithms and computational results on integer factorization. Includes links to
papers, downloadable software, and online resources.
http://www.crypto-world.com/FactorWorld.html
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The Anti-Divisor
A definition and description of the Anti-Divisor, and some related results.
http://www.users.globalnet.co.uk/~perry/maths
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Fermat Search
Leonid Durman's Fermat number factoring site and program.
http://www.fermatsearch.org/
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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.
http://www.alpertron.com.ar/ECM.HTM
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I Love Binary, Primes, and Factors
Divisibility, primes and binary numbers.
http://home.earthlink.net:80/~usondermann/binary.html
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Sam Wagstaff
Article about SNFS factorisation of 3^349-1.
http://www.purdue.edu/UNS/html4ever/9705.Wagstaff.number.html
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Integer Factorization
Paul Leyland's list of his own and other factorisations.
http://research.microsoft.com/~pleyland/factorization/main.htm
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N!+-1 Factoring Status
Factoring efforts that have been made so far on numbers of the form n!+-1 using ECM factoring.
http://www.uow.edu.au/~ajw01/ecm/curves.html
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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.
http://www.rsasecurity.com/rsalabs/challenges/factoring/index.html
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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.
http://www.prothsearch.net/sierp.html
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Robinson Primes
An analysis of problems relating to the numbers k.2^n+-1, primes, and factor patterns, including
the Sierpinski problem.
http://www.glasgowg43.freeserve.co.uk/robintro.htm
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Factorization of F10
F10 = 2^(2^10) + 1 is the 10-th Fermat number. Richard Brent details his discovery of the two
largest factors.
http://discus.anu.edu.au/~rpb/F10.html
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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.
http://www.math.uwaterloo.ca/~shallit/Papers/carissan.html
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Factoring Theory
A thorough summary of many major factoring algorithms. Includes some source code on many pages, and
gentle introductions to the more complex methods.
http://www.frenchfries.net/paul/factoring/theory/index.html
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The Factor Zone
Aimed at grade school students and teachers, includes course guidelines, worksheets, and factor
tables up to 600.
http://factorzone.tripod.com/
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Factoris
Online calculator that factorizes large numbers, specified by formula.
http://wims.unice.fr/~wims/wims.cgi?lang=en&module=tool/algebra/factor.en&cmd=new&
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