Factorizations of Cunningham numbers with bases 13 to 99: millenium edition

This Report updates the tables of factorizations of $a^n pm 1$ for $13 le a < 100$, previously published as CWI Report NM-R9212 (June 1992) and updated in CWI Report NM-R9419 (Update~1, September 1994) and CWI Report NM-9609 (Update~2, March 1996). A total of 951 this is an improvement by Tom Hill of an earlier new entries in the tables are given here. The factorizations are now complete for $n < 76$, was $n < 67$, and there are no composite cofactors smaller than $10^{102}$. This ``Millennium edition'' gives internet pointers to electronic versions of the complete tables incorporating all updates. A file containing only the new updates, a file containing factorizations for an extended table range, and a file of factors, are also available on the internet.