This site contains the paper, "The period of the Bell
exponential integers modulo a prime",
Proceedings of the Vancouver Conference, Mathematics of Computation
1943--1993, Proceedings of Symposia in Applied Mathematics,
v. 48 (1994), pp. 595--598. MR 95m:11030.

.pdf file for first paper on Bell numbers

This site also contains the paper, "Aurifeuillian factorizations
and the period of the Bell numbers modulo a prime",
Math. Comp. 65 (1996), pp. 383--391. MR 96f:11033.

Both papers were written by S. S. Wagstaff, Jr.

.pdf file for second paper on Bell numbers

The site also contains full versions of tables from these papers. They
give the known prime factors of the numbers (p^{p} - 1)/(p - 1) and
(p^{p} + 1)/(p + 1) with prime p < 180.

A third paper on Bell numbers, this one joint with Peter Montgomery
and Sangil Nahm, appeared in Math. Comp. 79 (2010), pp. 1793-1800.

See the .pdf file for the full third paper.

See the
.pdf file for slides from talk about this
third paper on Bell numbers I gave on September 25, 2009.

Also see the
.pdf file for slides from talk about this
third paper on Bell numbers I gave on May 27, 2011.

Please send me new prime factors of the numbers
in the following tables, but not factors of numbers with larger p.
A dollar sign ("$") at the end of a line means that the long integer
continues on the following line.

text file with factors of (p^{p} - 1)/(p - 1)

text file with factors of (p^{p} + 1)/(p + 1)

Send e-mail to Sam Wagstaff

#### (This page last modified March 22, 2017)