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On maximal gaps between successive primes


Author: Daniel Shanks
Journal: Math. Comp. 18 (1964), 646-651
MSC: Primary 10.42
DOI: https://doi.org/10.1090/S0025-5718-1964-0167472-8
MathSciNet review: 0167472
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  • [2] D. Shanks, Solved and Unsolved Problems in Number Theory, Vol. 1, Spartan, Washington, 1962, p. 201. MR 0160741 (28:3952)
  • [3] J. Barkley Rosser & Lowell Schoenfeld, ``Approximate formulas for some functions of prime numbers,'' Illinois J. Math., v. 6, 1962, p. 64-94. MR 0137689 (25:1139)
  • [4] Harald Cramér, ``On the order of magnitude of the difference between consecutive prime numbers,'' Acta Arith., v. 2, 1937, p. 23-46.
  • [5] D. H. Lehmer, ``Tables concerning the distribution of primes up to 37 millions,'' 1957, copy deposited in the UMT File and reviewed in MTAC, v. 13, 1959, p. 56-57.
  • [6] A. E. Western, ``Note on the magnitude of the difference between successive primes,'' J. London Math. Soc., v. 9, 1934, p. 276-278.
  • [7] J. W. L. Glaisher, ``On long successions of composite numbers,'' Messenger of Mathematics, v. 7, 1877, p. 102, 171.
  • [8] Kenneth I. Appel & J. Barkley Rosser, Table for Estimating Functions of Primes, IDA-CRD Technical Report Number 4, 1961, p. 102. (Reviewed in RMT 55, Math. Comp., v. 16, 1962, p. 500-501.)
  • [9] D. B. Gillies, ``Three new Mersenne primes and a statistical theory,'' Math. Comp., v. 18, 1964, p. 93. MR 0159774 (28:2990)
  • [10] Karl Prachar, Primzahlverteilung, Springer, Berlin, 1957, p. 154-164. MR 0087685 (19:393b)

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DOI: https://doi.org/10.1090/S0025-5718-1964-0167472-8
Article copyright: © Copyright 1964 American Mathematical Society

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