The files in this directory summarize the state of the Cunningham
project as of 29 July 1993

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

The factorizations of b^n + 1, for b = 2, 3, 5, 6, 7, 10, 11, 12 are
held in the files 2+, 3+ etc.  Likewise, the factorizations of b^n - 1
are held in 2-, 3- etc.

These files contain only primitive factors.  Some Aurifeuillean
factorizations have been listed separately; others are amalgamated.
By and large, the smaller ones are amalgamated.  For example, in the
10+ file, 10^50+1 is given as

50	60101.7019801.14103673319201.1680588011350901

but 10^150+1 as

150L	261301.38654658795718156456729958859629701
150M	601.3903901.168290119201.25074091038628125301

The notation P123 indicates a prime of 123 decimal digits, not
otherwise specified; C123 indicates a number of 123 decimal digits
known to be composite, but whose factors are not yet known.

(But see the files "primes.Z" and "composites.Z" -- these are not
necessarily kept quite so up to date as the main tables, they are also
kept compressed because they are so much bigger than the main
tables.).

I believe these tables are accurate and complete up to July 1993, but
would appreciate being told of any corrections and updates.

The file UPDATE will contain a series of changes to the files made
since the date specified in UPDATE.  Every now and again, that date
will be reset and the update started afresh.  I hope that makes sense.

Paul Leyland  pcl@ox.ac.uk