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These are tables of known factors of numbers of the form bn±1, with b={2, 3, 5, 6, 7, 10, 11, 12} (4, 8, and 9 would be redundant, but you already knew that). These were first created by Cunningham and Woodall in 1925, and have been expanded since then by many others.

Far more often than not, only a partial prime factorization is complete, with the cofactor indicated as a composite of a given length (e.g. c232 for a composite 232 digit number). Complete factorizations are the goal of the Cunningham Project, which is the ongoing search Cunningham's and Woodall's work has evolved into. It is located at http://www.cerias.purdue.edu/homes/ssw/cun/ . It is also the internet version of the print form of the tables, Factorizations of bn±1, b=2,3,5,6,7,10,11,12 up to high powers by J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman and S. S. Wagstaff, Jr.

The Cunningham Project and Cunningham tables will never be complete, but progress in it/them helps throughout number theory.

Related to these are the Brent-Montgomery-te Reile tables and the tables produced by Hisanori Mishima, Mitsuo Morimoto, Pete Moore, and Andy Steward.

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