"Homogeneous Cunningham numbers" is the term for 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 b < a ≤ 12 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 originally created by Bob Silverman. In April 2006, Bob sent them to Paul Leyland, who made them public and began to maintain them. With the factoring work of many people around the world, very few of the original numbers remained unfactored by the start of 2007. At that point some of the tables were extended to higher index, most of which were completed by mid-2009. A further extension was largely completed by March 2016, whereupon Paul and Jon Becker made an extension that set the upper limit on an ± bn to 1024 bits. Many relatively small factors were found by Jon and Paul before the extension tables were published. In 2018 Jon added Aurifeuillian factorizations to the tables, with the individual Aurifeuillian constituents also going up to a limit of 1024 bits. In October 2018 Jon took over maintenance of the tables.
The tables below use the the same format as the Cunningham tables, with some small exceptions. See the Formatting page for details.
Additions and corrections to the tables are welcome, and a number of people have already contributed further factorizations. Please send all such data to Jon. The file UPDATE contains a list of changes to the files made since 1 April 2016 and here are those reported before that date.
An ECMnet server (for version 2 clients only) is running on ecm.unshlump.com:8194. A status page for the server can be found here. It is updated once per day.
There are currently 470 composites in the tables.
a \ b