Prime clusters and Cunningham chains
Author:
Tony Forbes
Journal:
Math. Comp. 68 (1999), 17391747
MSC (1991):
Primary 11A41, 11Y11
Published electronically:
May 24, 1999
MathSciNet review:
1651752
Fulltext PDF Free Access
Abstract 
References 
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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 16tuplets and Cunningham chains of length 14.
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 L. E. Dickson, A new extension of Dirichlet's theorem on prime numbers, Messenger of Mathematics 33 (1904), 155161.
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 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), 170.
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 D. Hensley and I. Richards, Primes in intervals, Acta Arith. 25 (1974), 375391. MR 53:305
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 K.H. Indlekofer and A. Járai, Largest known twin primes, Math. Comp. 65 (1996), 427428. MR 96d:11009
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 Tony Forbes, Large prime triplets, Math. Spectrum 29 (1996/97), 65.
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 Warut Roonguthai, Large prime quadruplets, M500 153 (December 1996), 45.
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 A. O. L. Atkin, Personal communications, 9 June 1997 and earlier.
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 John Brillhart, D. H. Lehmer and J. L. Selfridge, New primality criteria and factorizations of , Math. Comp. 29 (1975), 620647. MR 52:5546
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 J. Brillhart et al., Factorizations of , , up to high powers, Contemporary Mathematics, vol. 22, 2nd ed., Amer. Math. Soc., 1988. MR 90d:11009
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 R. K. Guy, Unsolved problems in number theory, 2nd ed., SpringerVerlag, New York, 1994. MR 96e:11002
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 Tony Forbes, Prime tuplets15, M500 156 (July 1997), 1415.
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 Günter Löh, Long chains of nearly doubled primes, Math. Comp. 53 (1989), 751759. MR 90e:11015
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Additional Information
Tony Forbes
Affiliation:
22 St. Albans Road, Kingston upon Thames, Surrey, KT2 5HQ England
DOI:
http://dx.doi.org/10.1090/S0025571899011175
PII:
S 00255718(99)011175
Received by editor(s):
July 24, 1997
Published electronically:
May 24, 1999
Article copyright:
© Copyright 1999
American Mathematical Society
