Seven consecutive primes in arithmetic progression

Authors:
Harvey Dubner and Harry Nelson

Journal:
Math. Comp. **66** (1997), 1743-1749

MSC (1991):
Primary 11N13

DOI:
https://doi.org/10.1090/S0025-5718-97-00875-2

MathSciNet review:
1423071

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-97-00875-2

Received by editor(s):
January 30, 1996

Received by editor(s) in revised form:
August 16, 1996

Article copyright:
© Copyright 1997
American Mathematical Society