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

 

Seven consecutive primes in arithmetic progression


Authors: Harvey Dubner and Harry Nelson
Journal: Math. Comp. 66 (1997), 1743-1749
MSC (1991): Primary 11N13
MathSciNet review: 1423071
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Abstract: It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. In 1967, the first such sequence of 6 consecutive primes in arithmetic progression was found. Searching for 7 consecutive primes in arithmetic progression is difficult because it is necessary that a prescribed set of at least 1254 numbers between the first and last prime all be composite. This article describes the search theory and methods, and lists the only known example of 7 consecutive primes in arithmetic progression.


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Additional Information

Harvey Dubner
Affiliation: 449 Beverly Road, Ridgewood, New Jersey 07450
Email: 70327.1170@compuserve.com

Harry Nelson
Affiliation: 4259 Erory Way, Livermore, California 94550
Email: hln@anduin.ocf.llnl.gov

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00875-2
PII: S 0025-5718(97)00875-2
Received by editor(s): January 30, 1996
Received by editor(s) in revised form: August 16, 1996
Article copyright: © Copyright 1997 American Mathematical Society