Some of my more enjoyable collaborations in mathematical computations have been

• truly random numbers with Yaneer Bar-Yam,
• modular forms with Barry Brent,
• searching for Mersenne primes with Richard Crandall and others,
• a conjecture by Jean-Pierre Serre with Joe Buhler,
• large integer factoring with Mark Manasse and Carl Pomerance,
• Euler's generalization of Fermat's "Last Theorem" with Noam Elkies.
• random number generation with Franco Vitaliano.

My discovery of the smallest counter-example to Euler's Conjecture was published in

Supercomputing 88: Science and Applications
Edited by Joanne L. Martin and Stephen F. Lundstrom, page 106
"Finding 95800⁴ + 217519⁴ + 414560⁴ = 422481⁴ on the Connection Machine".
(Download Postscript 187KB)

The discovery was reported in the New York Times (April 17, 1988, page 28) and has been cited in several books, including Concrete Mathematics by Graham, Knuth, and Patashnik (page 131) and A New Kind of Science by Stephen Wolfram (page 945, top of column 2).