Euler’s constant to $1271$ places
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 Math. Comp. 16 (1962), 275281 Request permission
Abstract:
The value of Euler’s or Mascheroni’s constant \[ \gamma = \underset {n\to \infty }{\lim } (1 + \tfrac {1}{2} + \cdots + ({1}/{n})  \ln n)\] has now been determined to 1271 decimal places, thus extending the previously known value of 328 places. A calculation of partial quotients and best rational approximations to $\gamma$ was also made.References

L. Euler, “De progressionibus harmonicis observationes,” Euleri Opera Omnia Ser. 1, v. 14, Teubner, Leipzig and Berlin, 1925, p. 93100.
L. Euler, “De summis serierum numeros Bernoullianos involventium,” Euleri Opera Omnia Ser. 1, v. 15, Teubner, Leipzig and Berlin, 1927, p. 91130. See especially p. 115. The calculation is given in detail on p. 569583.
J. W. L. Glaisher, “On the calculation of Euler’s constant,” Proc. Roy. Soc. London, v. 19, 1870, p. 514524.
W. Shanks, “On the numerical value of Euler’s constant,” Proc. Roy. Soc. London, v. 15, 1867, p. 429432; v. 20, 1871, p. 2934.
J. W. L. Glaisher, “History of Euler’s constant,” Messenger of Mathematics, v. 1, 1872, p. 2530.
J. C. Adams, “On the value of Euler’s constant,” Proc. Roy. Soc. London, v. 27, 1878, p. 8894. See also v. 42, 1887, p. 2225.
K. Knopp, Theory and Application of Infinite Series, Blackie and Son, London, 1951, p. 257.
 J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708 J. W. Wrench, Jr., “A new calculation of Euler’s constant,” MTAC, v. 6, 1952, p. 255.
 David A. Pope and Marvin L. Stein, Multiple precision arithmetic, Comm. ACM 3 (1960), 652–654. MR 0116490, DOI 10.1145/367487.367499
 Daniel Shanks and John W. Wrench Jr., Calculation of $\pi$ to 100,000 decimals, Math. Comp. 16 (1962), 76–99. MR 136051, DOI 10.1090/S00255718196201360519 D. J. Wheeler, The Calculation of 60,000 Digits of e by the Illiac, Digital Computer Laboratory Internal Report No. 43, University of Illinois, Urbana, 1953.
 John W. Wrench Jr., Further evaluation of Khintchine’s constant, Math. Comp. 14 (1960), 370–371. MR 170455, DOI 10.1090/S00255718196001704551 R. S. Lehman, A Study of Regular Continued Fractions, Ballistic Research Lab. Report 1066, Aberdeen Proving Ground, Maryland, February 1959.
Additional Information
 © Copyright 1962 American Mathematical Society
 Journal: Math. Comp. 16 (1962), 275281
 MSC: Primary 10.41
 DOI: https://doi.org/10.1090/S0025571819620148255X
 MathSciNet review: 0148255