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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Evaluation of Artin’s constant and the twin-prime constant
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by John W. Wrench PDF
Math. Comp. 15 (1961), 396-398 Request permission
References
    A. J. C. Cunningham, “On the number of primes of the same residuacity,” Proc. London Math. Soc., ser. 2, v. 13, 1914, p. 258-272.
  • Herbert Bilharz, Primdivisoren mit vorgegebener Primitivwurzel, Math. Ann. 114 (1937), no. 1, 476–492 (German). MR 1513151, DOI 10.1007/BF01594189
  • Helmut Hasse, Vorlesungen über Zahlentheorie, Springer-Verlag, Berlin, 1950, p. 68-69.
  • 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, DOI 10.1007/BF02403921
  • Charles S. Sutton, “An investigation of the average distribution of twin prime numbers,” J. Math. Phys., v. 16, 1937, p. 1-42. C. R. Sexton, “Counts of twin primes less than 100 000,” MTAC, v. 8, 1954, p. 47-49. D. H. Lehmer, “Tables concerning the distribution of primes up to 37 millions,” deposited in UMT file. See MTAC, v. 13, 1959, p. 56-57 (Review 3). R. Liénard, Tables fondamentales à 50 décimales des sommes ${S_n}$, ${u_n}$, ${\Sigma _n}$, Centre de Documentation Universitaire, Paris, 1948.
  • A. Fletcher, J. C. P. Miller, and L. Rosenhead, An Index of Mathematical Tables, McGraw-Hill Book Co., New York; Scientific Computing Service Ltd., London, 1946. MR 0018419, DOI 10.1090/s0025-5718-45-99069-7
  • Carl-Erik Fröberg, “On the sum of inverses of primes and of twin primes,” Nordisk Mat. Tidskr. for Inf.-Behandling, v. 1, 1961, p. 15-20. Barkley Rosser, “The n-th prime is greater than $n\, \log \,n$,” Proc. London Math. Soc., v. 45, 1939, p. 21-44.
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Additional Information
  • © Copyright 1961 American Mathematical Society
  • Journal: Math. Comp. 15 (1961), 396-398
  • MSC: Primary 10.42
  • DOI: https://doi.org/10.1090/S0025-5718-1961-0124305-0
  • MathSciNet review: 0124305