The Cunningham project is described in the following excerpt from a
sci.math posting by Bob Silverman, who has contributed many of the
factorizations.
In 1925 Lt.-Col. Alan J.C. Cunningham and H.J. Woodall
gathered together all that was known about the primality and
factorization of such numbers and published a small book of tables.
"These tables collected from scattered sources the known prime factors
for the bases 2 and 10 and also presented the authors' results of
thirty years' work with these and the other bases" (see [1])
Since 1925 many people have worked on filling in these tables.
It is likely that this project is the longest, ongoing computational
project in history. D.H. Lehmer, a well known mathematician who passed
away in 1991 was for many years a leader of these efforts. Professor
Lehmer was a mathematician who was at the forefront of computing as
modern electronic computers became a reality. He was also known as the
inventor of some ingenious pre-electronic computing devices
specifically designed for factoring numbers. These devices are
currently in storage at the Computer Museum in Boston.
For a history of this project I suggest you obtain a copy of:
[1]:
J. Brillhart, D.H. Lehmer, J. Selfridge, S.S. Wagstaff Jr., &
B. Tuckerman Contemporary Mathematics vol 22, "Factorizations of
b^n +/-1, b = 2,3,5,6,7,10,11,12 up to high powers", published
by the American Math. Society 1983, 2nd Edition 1988