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Mathematics of Computation

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On maximal gaps between successive primes


Author: Daniel Shanks
Journal: Math. Comp. 18 (1964), 646-651
MSC: Primary 10.42
MathSciNet review: 0167472
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  • [1] E. Lucas, Théorie des Nombres, Vol. 1, Gauthier-Villars, Paris, 1891, p. 360.
  • [2] Daniel Shanks, Solved and unsolved problems in number theory. Vol. I, Spartan Books, Washington, D.C., 1962. MR 0160741
  • [3] J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. MR 0137689
  • [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] Donald B. Gillies, Three new Mersenne primes and a statistical theory, Math. Comp. 18 (1964), 93–97. MR 0159774, 10.1090/S0025-5718-1964-0159774-6
  • [10] Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0087685

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