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Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

Ten consecutive primes in arithmetic progression

Author(s): H. Dubner; T. Forbes; N. Lygeros; M. Mizony; H. Nelson; P. Zimmermann.
Journal: Math. Comp. 71 (2002), 1323-1328.
MSC (2000): Primary 11N13
Posted: November 28, 2001
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Abstract | References | Similar articles | Additional information

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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H. Dubner, The Size of Prime Factorials, J. Recreational Math. 19(1), 1987, pp. 743-749.

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L. J. Lander & T. R. Parkin, Consecutive Primes in Arithmetic Progression, Math. Comp. 21(1967), p. 489. MR 37:6237

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N. Lygeros & M. Mizony & P. Zimmermann, Sur la division euclidienne d'un nombre premier par son rang, Journée de Mathématiques Effectives, Départment de Mathématiques de l'Université Jean Monnet, Nov. 1998.

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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: 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
Posted: November 28, 2001
Copyright of article: Copyright 2001, American Mathematical Society


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