Factorizations of Cunningham numbers with bases 13 to 99

200. R. P. Brent, P. Montgomery and H. te Riele, Factorizations of Cunningham numbers with bases 13 to 99: Millennium edition, Report PRG TR-14-00, 31 December 2000, vi + 463 pp. arXiv:1004.3169v2

Report: dvi (424K), pdf (1041K), ps (681K).

Tables with extended exponent range: txt (552K).

Update 3 (original table range, includes updates from March 1996 to Dec 2000): txt (56K).

Preliminary version of Update 4 (original table range, includes updates from Jan 2001 to Oct 2003): txt (27K).


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 951 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 available from http://wwwmaths.anu.edu.au/~brent/factors.html .


This is Update 3 to the tables [134]. An abridged version appeared as Report MAS-R0107, CWI, Amsterdam, July 2001, 28 pp.


In the original Report's abstract and text (Table 1) we state that there are 943 new entries in the tables. A more accurate count reveals that the correct number is 951. (Thanks to Tom Hill for pointing out some errors in the update file which resulted in the new count.) These errors have been fixed in the online version of the report.

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