Programming Research Group Technical Report TR-14-00

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

Richard Brent, Peter L. Montgomery and Herman J.J. te Riele.

December 2000, 509 pp.

Abstract

This Report updates the tables of factorizations of an ± 1 for 13 <= 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-R9609 (Update 2, March 1996). A total of 943 new entries in the tables are given here. The factorizations are now complete for n < 76, and there are no composite cofactors smaller than 10102.

This "Millennium edition" gives 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 all available on the internet.

1991 Mathematics Subject Classification.
Primary 11A25; Secondary 11-04
Key words and phrases.
Cunningham numbers, elliptic curve method, factor tables, number field sieve, quadratic sieve, ECM, GNFS, MPQS, NFS, PMPQS, PPMPQS, SNFS
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