This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
Is there an arithmetic progression of 20 or more primes?
There is an arithmetic progression of 21 primes:
142072321123 + 1419763024680 i, 0 <= i < 21.
It was discovered on 30 November 1990, by programs running in the background
on a network of Sun 3 workstations in the Department of Computer Science,
University of Queensland, Australia.
See: Andrew Moran and Paul Pritchard, The design of a background job
on a local area network, Procs. 14th Australian Computer Science Conference,
1991, to appear.