"Homogeneous Cunninghman numbers" is the term I use for those numbers of the form an ± bn which seem not otherwise to have a name in the literature. Cunningham numbers proper take the form an ± 1, where a is an integer, not a prime power, between 2 and 12 inclusive. The tables below contain factorizations for 12 ≥ a > b and gcd (a, b) = 1. The tables for 9n ± 4n are omitted because they are but subsets of the tables for 3n ± 2n
These tables were supplied to me by Bob Silverman in April 2006. Very few of the original numbers remained unfactored by the start of 2007 and so some of the tables were extended to higher index. The tables below contain Bob's data, together with my extensions and the factors supplied by numerous workers, split into separate files and converted to my standard format, designed to be both human-readable and easily parsed by programs.
I welcome additions and corrections to the tables and a number of people have already contributed further factorizations. The file UPDATE contains a list of changes to the files made since 23 December 2007 and here are those reported to me before that date.
These numbers are now loaded into the ECMNET server hosted by Phil Carmody at port 8194 on the machine 83.143.57.194. The ECMNET software itself was written by Mark Rodenkirch
ECM users may find a gzipped list of all the composite cofactors useful. There are 265 numbers in this file.
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