On maximal gaps between successive primes
Author:
Daniel Shanks
Journal:
Math. Comp. 18 (1964), 646651
MSC:
Primary 10.42
MathSciNet review:
0167472
Fulltext PDF Free Access
References 
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Additional Information
 [1]
E. Lucas, Théorie des Nombres, Vol. 1, GauthierVillars, Paris, 1891, p. 360.
 [2]
Daniel
Shanks, Solved and unsolved problems in number theory. Vol. I,
Spartan Books, Washington, D.C., 1962. MR 0160741
(28 #3952)
 [3]
J.
Barkley Rosser and Lowell
Schoenfeld, Approximate formulas for some functions of prime
numbers, Illinois J. Math. 6 (1962), 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. 2346.
 [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. 5657.
 [6]
A. E. Western, ``Note on the magnitude of the difference between successive primes,'' J. London Math. Soc., v. 9, 1934, p. 276278.
 [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, IDACRD Technical Report Number 4, 1961, p. 102. (Reviewed in RMT 55, Math. Comp., v. 16, 1962, p. 500501.)
 [9]
Donald
B. Gillies, Three new Mersenne primes and a
statistical theory, Math. Comp. 18 (1964), 93–97. MR 0159774
(28 #2990), http://dx.doi.org/10.1090/S00255718196401597746
 [10]
Karl
Prachar, Primzahlverteilung, SpringerVerlag, Berlin, 1957
(German). MR
0087685 (19,393b)
 [1]
 E. Lucas, Théorie des Nombres, Vol. 1, GauthierVillars, Paris, 1891, p. 360.
 [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. 6494. 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. 2346.
 [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. 5657.
 [6]
 A. E. Western, ``Note on the magnitude of the difference between successive primes,'' J. London Math. Soc., v. 9, 1934, p. 276278.
 [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, IDACRD Technical Report Number 4, 1961, p. 102. (Reviewed in RMT 55, Math. Comp., v. 16, 1962, p. 500501.)
 [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. 154164. MR 0087685 (19:393b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196401674728
PII:
S 00255718(1964)01674728
Article copyright:
© Copyright 1964 American Mathematical Society
