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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References | Similar Articles | Additional Information

**[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**, https://doi.org/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:
https://doi.org/10.1090/S0025-5718-1964-0167472-8

Article copyright:
© Copyright 1964
American Mathematical Society