Prime clusters and Cunningham chains

Forbes, Tony

doi:10.1090/S0025-5718-99-01117-5

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
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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 396440, https://doi.org/10.4064/aa-25-4-375-391
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 384673, 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 $k$ -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