Prime clusters and Cunningham chains

Author:
Tony Forbes

Journal:
Math. Comp. **68** (1999), 1739-1747

MSC (1991):
Primary 11A41, 11Y11

DOI:
https://doi.org/10.1090/S0025-5718-99-01117-5

Published electronically:
May 24, 1999

MathSciNet review:
1651752

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss the methods and results of a search for certain types of prime clusters. In particular, we report specific examples of prime 16-tuplets and Cunningham chains of length 14.

**1.**L. E. Dickson,*A new extension of Dirichlet's theorem on prime numbers*, Messenger of Mathematics**33**(1904), 155-161.**2.**G. H. Hardy and J. E. Littlewood,*Some problems of `Partitio Numerorum'; III: On the expression of a number as a sum of primes*, Acta Math.**44**(1922), 1-70.**3.**Douglas Hensley and Ian Richards,*Primes in intervals*, Acta Arith.**25**(1973/74), 375–391. MR**0396440****4.**D. M. Gordon and G. Rodemich,*Dense admissible sets*, Algorithmic Number Theory: III; Lecture Notes in Computer Science, Volume 1423, Springer Verlag, Berlin, 1998.**5.**C. K. Caldwell and H. Dubner,*Primorial, factorial and multifactorial primes*, Math. Spectrum**26**(1993/94), 1-7.**6.**Karl-Heinz Indlekofer and Antal Járai,*Largest known twin primes*, Math. Comp.**65**(1996), no. 213, 427–428. MR**1320896**, https://doi.org/10.1090/S0025-5718-96-00666-7**7.**Tony Forbes,*Large prime triplets*, Math. Spectrum**29**(1996/97), 65.**8.**Warut Roonguthai,*Large prime quadruplets*, M500**153**(December 1996), 4-5.**9.**A. O. L. Atkin, Personal communications, 9 June 1997 and earlier.**10.**John Brillhart, D. H. Lehmer, and J. L. Selfridge,*New primality criteria and factorizations of 2^{𝑚}±1*, Math. Comp.**29**(1975), 620–647. MR**0384673**, https://doi.org/10.1090/S0025-5718-1975-0384673-1**11.**John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, and S. S. Wagstaff Jr.,*Factorizations of 𝑏ⁿ±1*, 2nd ed., Contemporary Mathematics, vol. 22, American Mathematical Society, Providence, RI, 1988. 𝑏=2,3,5,6,7,10,11,12 up to high powers. MR**996414****12.**Richard K. Guy,*Unsolved problems in number theory*, 2nd ed., Problem Books in Mathematics, Springer-Verlag, New York, 1994. Unsolved Problems in Intuitive Mathematics, I. MR**1299330****13.**Tony Forbes,*Prime -tuplets-15*, M500**156**(July 1997), 14-15.**14.**Günter Löh,*Long chains of nearly doubled primes*, Math. Comp.**53**(1989), no. 188, 751–759. MR**979939**, https://doi.org/10.1090/S0025-5718-1989-0979939-8

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Additional Information

**Tony Forbes**

Affiliation:
22 St. Albans Road, Kingston upon Thames, Surrey, KT2 5HQ England

DOI:
https://doi.org/10.1090/S0025-5718-99-01117-5

Received by editor(s):
July 24, 1997

Published electronically:
May 24, 1999

Article copyright:
© Copyright 1999
American Mathematical Society