The files in this directory summarize the state of the Cunningham
project as of 29 July 1998.

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.gz" and "composites.gz" -- 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.  Neither do they contain data for some of the more recent
extensions to the tables.  These files may become more complete in the
future, but don't rely on it.)

I believe these tables are accurate and complete up to the end of July 1998,
but would appreciate being told of any corrections and updates.  With
almost 8000 entries in total, there is a fair chance that I have made
transcription and other errors.

Acknowledgements:  As well as all the factorers, far too many to mention
individually, I'd particularly like to thank Sam Wagstaff for making his
extensive tables available to me.  Indeed, my version is essentially his
tables, reformatted to make them easier to parse by factoring programs.


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  pleyland@microsoft.com