Cunningham project
In 1925 Cunningham and Woodall published a table of the known factors of bn+/-1 (b =2, 3, 5, 6, 7, 10, 11 and 12) for various ranges of n. These numbers include many of the standard forms, including the Mersennes, Fermats, and repunits. The work of completing and extending these factorizations is often called the Cunningham project. The current status of the project can be found online or in the book by Brillhart et. al. (below).
The Cunningham project provides a fertile testing ground for new advances in the theory of factoring and primality proving. Some of the algorithms that are theoretically the fastest are just not currently practical. So if you want to know what is hot (and what is not) in the world of factoring, just look to see what folks are using to find factors for this project.
The Cunningham project will never be finished. As our ability to factor improves, the range of the exponents is increased!
Related pages (outside of this work)
References:
- BLSTW88
- J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman and S. S. Wagstaff, Jr., Factorizations of bn ± 1, b=2,3,5,6,7,10,12 up to high powers, Amer. Math. Soc., 1988. Providence RI, pp. xcvi+236, ISBN 0-8218-5078-4. MR 90d:11009 (Annotation available)