Long chains of nearly doubled primes

Author:
Günter Löh

Journal:
Math. Comp. **53** (1989), 751-759

MSC:
Primary 11A41; Secondary 11Y11

DOI:
https://doi.org/10.1090/S0025-5718-1989-0979939-8

MathSciNet review:
979939

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Abstract | References | Similar Articles | Additional Information

Abstract: A chain of nearly doubled primes is an ordered set of prime numbers, interlinked by . A search for long chains of this kind has been performed in the range . Chains of length up to 13 have been found. Shorter chains have been counted in some restricted ranges. Some of these counts are compared with the frequencies predicted by a quantitative version of the prime *k*-tuples conjecture.

**[1]**Paul T. Bateman and Roger A. Horn,*A heuristic asymptotic formula concerning the distribution of prime numbers*, Math. Comp.**16**(1962), 363–367. MR**148632**, https://doi.org/10.1090/S0025-5718-1962-0148632-7**[2]**Allan Cunningham, "On hyper-even numbers and on Fermat's numbers,"*Proc. London Math. Soc. (2)*, v. 5, 1907, pp. 237-274.**[3]**Richard K. Guy,*Unsolved problems in number theory*, Unsolved Problems in Intuitive Mathematics, vol. 1, Springer-Verlag, New York-Berlin, 1981. Problem Books in Mathematics. MR**656313****[4]**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**(1923), no. 1, 1–70. MR**1555183**, https://doi.org/10.1007/BF02403921**[5]**Claude Lalout & Jean Meeus, "Nearly-doubled primes,"*J. Recreational Math.*, v. 13, 1980-81, pp. 30-35.**[6]**D. H. Lehmer,*On certain chains of primes*, Proc. London Math. Soc. (3)**14a**(1965), 183–186. MR**0177964**, https://doi.org/10.1112/plms/s3-14A.1.183**[7]**Daniel Gallin, R. P. Nederpelt, R. B. Eggleton, John H. Loxton, A. Oppenheim, M. J. Pelling, Paul Erdos, and Jeffrey L. Rackusin,*Problems and Solutions: Elementary Problems: E2647-E2652*, Amer. Math. Monthly**84**(1977), no. 4, 294–295. MR**1538330**, https://doi.org/10.2307/2318876**[8]**Paulo Ribenboim,*13 lectures on Fermat’s last theorem*, Springer-Verlag, New York-Heidelberg, 1979. MR**551363****[9]**Hans Riesel,*Prime numbers and computer methods for factorization*, Progress in Mathematics, vol. 57, Birkhäuser Boston, Inc., Boston, MA, 1985. MR**897531****[10]**A. Schinzel & W. Sierpiński, "Sur certaines hypothèses concernant les nombres premiers,"*Acta Arith.*, v. 4, 1958, pp. 185-208. MR**21**#4936.**[11]**Takao Sumiyama, "Cunningham chains of length 8 and 9,"*Abstracts Amer. Math. Soc.*, v. 4, 1983, p. 192, 83T-05-72.**[12]**Takao Sumiyama, "The distribution of Cunningham chains,"*Abstracts Amer. Math. Soc.*, v. 4, 1983, p. 489, 83T-10-405.**[13]**Samuel Yates,*Repunits and repetends*, Samuel Yates, Delray Beach, Fla., 1982. With a foreword by D. H. Lehmer. MR**667020**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1989-0979939-8

Keywords:
Nearly doubled primes,
prime chains,
Cunningham chains,
prime *k*-tuples conjecture

Article copyright:
© Copyright 1989
American Mathematical Society