Available in electronic format
Available in print format
Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

Prime clusters and Cunningham chains

Author(s): Tony Forbes.
Journal: Math. Comp. 68 (1999), 1739-1747.
MSC (1991): Primary 11A41, 11Y11
Posted: May 24, 1999
Retrieve article in: PDF
This article is available free of charge

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.


References:

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.
D. Hensley and I. Richards, Primes in intervals, Acta Arith. 25 (1974), 375-391. MR 53:305

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.
K.-H. Indlekofer and A. Járai, Largest known twin primes, Math. Comp. 65 (1996), 427-428. MR 96d:11009

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 $2^m\pm 1$, Math. Comp. 29 (1975), 620-647. MR 52:5546

11.
J. Brillhart et al., Factorizations of $b^n\pm 1$, $b=2,3,5,6,7,10,11,12$, up to high powers, Contemporary Mathematics, vol. 22, 2nd ed., Amer. Math. Soc., 1988. MR 90d:11009

12.
R. K. Guy, Unsolved problems in number theory, 2nd ed., Springer-Verlag, New York, 1994. MR 96e:11002

13.
Tony Forbes, Prime $k$-tuplets-15, M500 156 (July 1997), 14-15.

14.
Günter Löh, Long chains of nearly doubled primes, Math. Comp. 53 (1989), 751-759. MR 90e:11015


Similar Articles:

Retrieve articles in Mathematics of Computation with MSC (1991): 11A41, 11Y11

Retrieve articles in all Journals with MSC (1991): 11A41, 11Y11


Additional Information:

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

DOI: 10.1090/S0025-5718-99-01117-5
PII: S 0025-5718(99)01117-5
Received by editor(s): July 24, 1997
Posted: May 24, 1999
Copyright of article: Copyright 1999, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google