Note (9 Jan 2013)

Instead of sending your new factors to me, please add them to Jonathan's online list (or, if you have a large batch of factors, contact Jonathan directly).

I will continue to update a list of "ECM champs" for the time being (Paul Zimmermann also keeps a similar list).

Any "Cunningham numbers" (for bases up to 12) should continue to be sent to Sam Wagstaff.

Factor Tables

n satisfies the constraint aⁿ < 10²⁵⁵.

All the tables (as at 31 December 2000) can be obtained in one compressed text file from ../rpb200t.txt.gz

The file comps.gz contains 448 composite factors of numbers of the above form. If you factor any of these, please let Jonathan Crombie know. The composites are sorted by increasing size but I suggest that you do not start attempts to factor them from the beginning - if everyone does that too much effort will be put into the numbers near the beginning of the list. Better would be to choose a random starting point in the list.

The file ecmnet.txt contains a list of factors found by ECM (mainly by ECMNET) for bases 13..99 since 4 November 2003.

The file factors.gz contains 385,251 factors f of numbers aⁿ +- 1, where a < 10000, n < 10000, and f > 10⁹. For a < 12 these are mainly from the Cunningham tables (for n up to 1200), with contributions from Arjen Bot, Will Edgington, Alexander Kruppa and Paul Leyland (for larger n); for 13 < a < 99 they are mainly from the Brent-Montgomery-te Riele extension of the Cunningham tables, with contributions by ECMNET and various individuals (see below); for 100 < a < 1000 they are mainly from the tables produced by Hisanori Mishima and Mitsuo Morimoto with additions from Jonathan Crombie, Rob Hooft, Pete Moore and others. For prime bases a < 1000 I computed many of the factors for an unpublished extension of the Brent-Montgomery-te Riele tables. For updates, see Jonathan Crombie's list.

The file holes.txt contains a list of "first holes" in the tables of factors of numbers aⁿ +- 1, for a < 100. For updates, see Jonathan Crombie's list.

The files rpb117*.* and rpb134*.* may be useful.

Acknowledgements

Related Tables and Pages

• The Cunningham tables.
• The ECMNET home page and Mark Rodenkirch's ECM client/server page.
• Arjen Bot's lists of factors of 2ⁿ+-1 for n > 1200.
• The CADO-NFS page.
• Chris Caldwell's list of Mersenne primes.
• Clare's elementary introduction to factoring.
• Scott Contini's FactorWorld page (with pointers to papers on factorisation, historical information, and other relevant web pages).
• Jonathan Crombie's online factor collection.
• Torbjörn Granlund's lists of factors of 10ⁿ+-1.
• Makato Kamada's pages on factors of numbers of the form 10ⁿ + 1.
• Wilfrid Keller's list of known factors of Fermat numbers.
• Yousuke Koide's list of repunit factors.
• Factors of cyclotomic numbers by Tomoya Adachi ; also by Hisanori Mishima and Mitsuo Morimoto.
• The Odd Perfect Number page.
• Henrik Olsen's Number Field Sieve Net page.
• Tomás Oliveira e Silva's Goldbach conjecture verification page.
• My list of ECM champs (large factors found by the elliptic curve method), updated 6 January 2013.
• Paul Zimmermann's similar lists for the ECM, p-1 and p+1 methods.
• Paul Zimmermann's factoring records page.
• Paul Zimmermann's list of ECM software.
• Markus Tervooren's factordb.com online factor database.

( ../rpb200t.txt.gz updated 18 January 2001)
( comps.gz updated 14 Jan 2013 by Jonathan Crombie)
( ecmnet.txt updated 1 March 2007)
( factors.gz updated 16 Sept 2011)
( holes.txt updated 5 May 2011)

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