Factor Tables

The directory http://wwwmaths.anu.edu.au/~brent/ftp/factors/
and its parent directory contain tables related to factors of an +- 1 for a = 13, 14, ... , 99 (perfect powers excluded).

n satifies 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 955 composite factors of numbers of the above form. If you factor any of these, please let me 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 276,367 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 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 1000 I computed many of the factors for an unpublished extension of the Brent-Montgomery-te Riele tables.

The file holes.txt contains a list of "first holes" in the tables of factors of numbers an +- 1, for a < 100.

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

Acknowledgements

Many people have contributed to the factor tables. In particular, I would like to thank: Tomoya Adachi, Franz-Dieter Berger, Aniruddha Bhargava, Henk Boender, Arjen Bot, Dominique Bugmann, John Cannon, Stephania Cavallar, Tim Charron, Graeme Cohen, Conrad Curry, Nicolas Daminelli, Thomas Denny, Bruce Dodson, Harvey Dubner, ECMNET (some contributors also listed individually), Will Edgington, 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, A. McFarlane, David Miller, Hisanori Mishima, Hunter Monroe, Peter Montgomery, Pete Moore, Mitsuo Morimoto, Andreas Müller, Henrik Olsen, J. Pawlewicz, Sylvain Pelissier, John Pollard, R. Propper, Alfred Reich, Herman te Riele, Hans Riesel, David Rusin, Jukka Santala, George Sassoon, M. Schroeder, Bob Silverman, Thomas Sosnowski, Holger Spielmann, Allan Steel, Andy Steward, 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
email: Firstname.Lastname@anu.edu.au

( ../rpb200t.txt.gz updated 18 January 2001)
( comps.gz updated 8 April 2008)
( ecmnet.txt updated 22 February 2007)
( factors.gz updated 7 July 2008)
( holes.txt updated 7 July 2008)

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