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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Ten consecutive primes in arithmetic progression


Authors: H. Dubner, T. Forbes, N. Lygeros, M. Mizony, H. Nelson and P. Zimmermann
Journal: Math. Comp. 71 (2002), 1323-1328
MSC (2000): Primary 11N13
Published electronically: November 28, 2001
MathSciNet review: 1898760
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Abstract: In 1967 the first set of 6 consecutive primes in arithmetic progression was found. In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we succeeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progression. This was made possible because of the increase in computer capability and availability, and the ability to obtain computational help via the Internet. Although it is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression, it is very likely that 10 primes will remain the record for a long time.


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Additional Information

H. Dubner
Affiliation: 449 Beverly Road, Ridgewood, New Jersey 07450
Email: hdubner1@compuserve.com

T. Forbes
Affiliation: 22 St. Albans Road, Kingston upon Thames, Surrey, KT2 5HQ England
Email: tonyforbes@ltkz.demon.co.uk

N. Lygeros
Affiliation: Institut Girard, Cnr Upres-A 502B, Université Lyon I 43 Bd Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
Email: lygeros@desargues.univ-lyon1.fr

M. Mizony
Affiliation: Institut Girard, Cnr Upres-A 502B, Université Lyon I 43 Bd Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
Email: mizony@desargues.univ-lyon1.fr

H. Nelson
Affiliation: 4259 Emory Way, Livermore, California 94550
Email: hlnel@flash.net

P. Zimmermann
Affiliation: Inria Lorraine, Technopole de Nancy-Brabois, 615 Rue Du Jardin Botanique Bp 101, F-54600 Villers-Lès-Nancy, France
Email: zimmerma@loria.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01374-6
PII: S 0025-5718(01)01374-6
Keywords: Consecutive primes, arithmetic progression
Received by editor(s): June 22, 1998
Received by editor(s) in revised form: October 10, 2000
Published electronically: November 28, 2001
Article copyright: © Copyright 2001 American Mathematical Society