Note (9 Jan 2013)

After doing it for more than 30 years (approximately since my 1981 factorization of F8 with John Pollard) I have retired from the task of collecting factors. Jonathan Crombie has volunteered to take over. (Thanks Jonathan!)

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

The directory
and its parent directory contain tables related to factors of an +- 1 for a = 13, 14, ... , 99 (perfect powers excluded).

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 1000 I computed many of the factors for an unpublished extension of the Brent-Montgomery-te Riele tables.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.


Many people have contributed to the factor tables. In particular, I would like to thank: Tomoya Adachi, Franz-Dieter Berger, Aniruddha Bhargava, Henk Boender, Joppe Bos, Arjen Bot, Dominique Bugmann, John Cannon, Stephania Cavallar, Tim Charron, Chris Chris, Graeme Cohen, Jonathan Crombie, Conrad Curry, Nicolas Daminelli, Thomas Denny, Bruce Dodson, Harvey Dubner, ECMNET (some contributors also listed individually), Will Edgington, Al Edwards, Willemien Ekkelkamp, Jens Franke, Reuven Gevaryahu, Torbjörn Granlund, Tom Hill, Uwe Hollerbach, Rob Hooft, Marije Huizing, Pierre Jammes, Makato Kamada, Wilfrid Keller, Yuji Kida, Thorsten Kleinjung, Tetsuya Kobayashi, Yousuke Koide, Alexander Kruppa, Hidenori Kuwakado, Jocelyn Larouche, Samuli Larvala, Joe Leherbauer, Arjen Lenstra, Paul Leyland, Walter Lioen, William Lipp, A. McFarlane, David Miller, Hisanori Mishima, Hunter Monroe, Peter Montgomery, Pete Moore, Mitsuo Morimoto, Andreas Müller, Henrik Olsen, Oscar Ostlin, J. Pawlewicz, Sylvain Pelissier, John Pollard, R. Propper, Alfred Reich, Herman te Riele, Hans Riesel, Mark Rodenkirch, Warut Roonguthai, David Rusin, Jukka Santala, George Sassoon, M. Schroeder, Bob Silverman, Thomas Sosnowski, Holger Spielmann, Allan Steel, Mathew Stein, Andy Steward, Ken Takusagawa, Markus Tervooren, Rocke Verser, Sam Wagstaff, Georg Wambach, Damian Weber, Michael Wiener, Hugh Williams, Aiichi Yamasaki, and Paul Zimmermann for their assistance. Apologies if I have forgotten anyone. If you have sent me factors and I have forgotten to acknowledge you here, please let me know!

Related Tables and Pages

The following may be of interest: Richard P. Brent

( ../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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