Brun's constant

Authors:
Daniel Shanks and John W. Wrench

Journal:
Math. Comp. **28** (1974), 293-299

MSC:
Primary 10H15; Secondary 10H25

DOI:
https://doi.org/10.1090/S0025-5718-1974-0352022-X

Corrigendum:
Math. Comp. **28** (1974), 1183-1184.

MathSciNet review:
0352022

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Abstract | References | Similar Articles | Additional Information

Abstract: This note reviews previous work and presents new numerical data and analytical development concerning a constant that arises in Brun's famous theorem about twin primes.

**[1]**Edgar Karst,*The Third*2500*Reciprocals and Their Partial Sums of all Twin Primes**between*(239429, 239431)*and*(393077, 393079). See UMT 8, page 332, this issue.**[2]**Daniel Shanks & Carol Neild,*Brun's Constant*. See UMT, 9, page 332, this issue.**[3]**Edmund Landau,*Elementare Zahlentheorie*, Teubner, Leipzig, 1927; English transl. Chelsea, New York, 1958, p. 94. MR**19**, 1159.**[4]**Ernst S. Selmer,*A special summation method in the theory of prime numbers and its application to “Brun’s sum.”*, Norsk. Mat. Tidsskr.**24**(1942), 74–81 (Norwegian). MR**0018688****[5]**C. E. Fröberg, "On the sum of inverses of primes and of twin primes,"*Nordisk Tidskr. Informationsbehandling*(*BIT*), v. 1, 1961, pp. 15-20.**[6]**Viggo Brun, "La série , où les dénominateurs sont 'nombres premiers jumeaux' est convergente ou finie,"*Bull. Sci. Math.*, v. 43, 1919, pp. 124-128.**[7]**Edgar Karst,*The First*2500*Reciprocals and their Partial Sums of all Twin Primes**between*(3, 5)*and*(102761, 102763), UMT 52,*Math. Comp.*, v. 23, 1969, p. 686.**[8]**Edgar Karst,*The Second*2500*Reciprocals and their Partial Sums of all Twin Primes**between*(102911, 102913)*and*(239387, 239389), UMT 35,*Math. Comp.*, v. 26, 1972, p. 806.**[9]**Sol Weintraub,*Four Tables Concerning the Distribution of Primes*, UMT 38,*Math. Comp.*, v. 27, 1973, pp. 676-677.**[10]**John W. Wrench Jr.,*Evaluation of Artin’s constant and the twin-prime constant*, Math. Comp.**15**(1961), 396–398. MR**0124305**, https://doi.org/10.1090/S0025-5718-1961-0124305-0**[11]**Daniel Shanks,*Quadratic residues and the distribution of primes*, Math. Tables Aids Comput.**13**(1959), 272–284. MR**0108470**, https://doi.org/10.1090/S0025-5718-1959-0108470-8**[12]**F. Gruenberger & G. Armerding, "Statistics on the first six million primes," UMT 73,*Math. Comp.*, v. 19, 1965, pp. 503-505.**[13]**Hans Riesel and Gunnar Göhl,*Some calculations related to Riemann’s prime number formula*, Math. Comp.**24**(1970), 969–983. MR**0277489**, https://doi.org/10.1090/S0025-5718-1970-0277489-3**[14]**Richard P. Brent,*The distribution of small gaps between successive primes*, Math. Comp.**28**(1974), 315–324. MR**0330017**, https://doi.org/10.1090/S0025-5718-1974-0330017-X

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DOI:
https://doi.org/10.1090/S0025-5718-1974-0352022-X

Article copyright:
© Copyright 1974
American Mathematical Society