These tables are an extension to the Cunningham tables and consist of factorizations of bn±1, with 13<b<99, except for perfect powers. Primary credit for these goes to Richard P. Brent, Peter L. Montgomery, and Herman J. J. te Reile, whom these tables are named after.
These were first published in 1992, with updates dated September 1994, March 1996, December 31, 2000, and May 31 2002, as well as a second edition of the tables with the first three updates included December 31, 2000.
These tables include partial or complete factorizations of numbers within these bounds:
- 13≤a<30, exponents n such that an<10255
- 30≤a<100, exponents n≤100
The Brent-Montgomery-te Reile tables use the same notation as the Cunningham tables, denoting the largest factor as a single letter and its number of digits (e.g. c232 for a 232-digit composite, and p232 for a 232-digit prime). These factors are found by dividing the original number by all the other factors.
These tables, along with the Cunningham tables, are expanded primarily by various methods of factoring, particularly ECM (Elliptic Curve Method), GNFS(General Number Field Sieve), and SNFS (Special Number Field Sieve). These tables have been worked on less, so many of the composite cofactors are smaller than those found in the Cunningham Project, but most are more than 100 digits long.
Richard Brent maintains the official tables, and has them available on his web site at http://web.comlab.ox.ac.uk/oucl/work/richard.brent/factors.html