On the Computation of Euler’s Constant

  • Dura W. Sweeney


The computation of Euler’s constant, γ, to 3566 decimal places by a procedure not previously used is described. As a part of this computation, the natural logarithm of 2 has been evaluated to 3683 decimal places. A different procedure was used in computations of γ performed by J. C. Adams in 1878 [1] and J. W. Wrench, Jr. in 1952 [2], and recently by D. E. Knuth [3]. This latter procedure is critically compared with that used in the present calculation. The new approximations to γ and In 2 are reproduced in extenso at the, end of this paper.


Decimal Place Individual Term Bernoulli Number Multiplication Loop Intermediate Computation 
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  1. 1.
    J. C. Adams, “On the value of Euler’s constant,” Proc. Roy. Soc. London, v. 27, 1878, p. S8–94.Google Scholar
  2. 2.
    J. W. Wrench, JR., “A new calculation of Euler’s constant,” MTAC, v. 6, 1952. p. 255.Google Scholar
  3. 3.
    D. E. Iinuth, “Euler’s constant to 1271 places,” Math. Camp., v. 16, 1962, p. 275–281.Google Scholar
  4. 4.
    H. S. Uhler, “Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7, and 17,” Proc. Nat. Acad. Sci., v. 26. 1940, p. 205–212.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Dura W. Sweeney
    • 1
  1. 1.IBM Data Processing DivisionPoughkeepsieUSA

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