Prime clusters and Cunningham chains
HTML articles powered by AMS MathViewer
- by Tony Forbes PDF
- Math. Comp. 68 (1999), 1739-1747 Request permission
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
- L. E. Dickson, A new extension of Dirichlet’s theorem on prime numbers, Messenger of Mathematics 33 (1904), 155–161.
- 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.
- Douglas Hensley and Ian Richards, Primes in intervals, Acta Arith. 25 (1973/74), 375–391. MR 396440, DOI 10.4064/aa-25-4-375-391
- D. M. Gordon and G. Rodemich, Dense admissible sets, Algorithmic Number Theory: III; Lecture Notes in Computer Science, Volume 1423, Springer Verlag, Berlin, 1998.
- C. K. Caldwell and H. Dubner, Primorial, factorial and multifactorial primes, Math. Spectrum 26 (1993/94), 1–7.
- Karl-Heinz Indlekofer and Antal Járai, Largest known twin primes, Math. Comp. 65 (1996), no. 213, 427–428. MR 1320896, DOI 10.1090/S0025-5718-96-00666-7
- Tony Forbes, Large prime triplets, Math. Spectrum 29 (1996/97), 65.
- Warut Roonguthai, Large prime quadruplets, M500 153 (December 1996), 4–5.
- A. O. L. Atkin, Personal communications, 9 June 1997 and earlier.
- 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 384673, DOI 10.1090/S0025-5718-1975-0384673-1
- John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, and S. S. Wagstaff Jr., Factorizations of $b^n \pm 1$, 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, DOI 10.1090/conm/022
- 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, DOI 10.1007/978-1-4899-3585-4
- Tony Forbes, Prime $k$-tuplets—15, M500 156 (July 1997), 14–15.
- Günter Löh, Long chains of nearly doubled primes, Math. Comp. 53 (1989), no. 188, 751–759. MR 979939, DOI 10.1090/S0025-5718-1989-0979939-8
Additional Information
- Tony Forbes
- Affiliation: 22 St. Albans Road, Kingston upon Thames, Surrey, KT2 5HQ England
- Received by editor(s): July 24, 1997
- Published electronically: May 24, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1739-1747
- MSC (1991): Primary 11A41, 11Y11
- DOI: https://doi.org/10.1090/S0025-5718-99-01117-5
- MathSciNet review: 1651752