On August 29 1995, Harvey Dubner and Harry Nelson discovered
seven
consecutive primes in arithmetic progression, namely p, p +
210, p + 420, p + 630, p + 840, p + 1050 and
p + 1260 where p is the 97-digit number:
1089533431247059310875780378922957732908036492993138195385213105561742150447308967213141717486151.
On 7 November 1997, we - Harvey Dubner, Tony Forbes, Nik Lygeros, Michel Mizony and Paul Zimmermann - announced the discovery of eight consecutive primes in arithmetic progression after a search lasting a couple of months using a variety of PC's and Unix workstations.
We then initiated a search for nine primes, calling on the help of about a hundred people world-wide and using about 200 computers. On 15 January 1998, this search ended successfully when Manfred Toplic of Klagenfurt, Austria, found nine consecutive primes in arithmetic progression using Tony's program CP09.EXE on a PC.
References:
Harvey Dubner and Harry Nelson, "Seven primes in arithmetic progression", Mathematics of Computation, October 1997. Also available as a postscript file.
Harvey Dubner, Tony Forbes and Paul Zimmermann, "8 consec. primes in AP", NMBRTHRY, November 1997.
Harvey Dubner, Tony Forbes, Nik Lygeros, Michel Mizony and Paul Zimmermann, "9 consecutive primes in arithmetic progression", NMBRTHRY, January 1998.
Richard K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, 1994, 2nd edition, Section A.6.
Paulo Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1995, 3rd edition, Section IV.C.
E-mail addresses:
Harvey Dubner <HDubner1@compuserve.com>
Tony Forbes <tonyforbes@ltkz.demon.co.uk>
Michel Mizony <mizony@desargues.univ-lyon1.fr>
Nik Lygeros <lygeros@desargues.univ-lyon1.fr>
Paul Zimmermann <paul.zimmermann@loria.fr>