Number of digits  When  Who  Notes 

5  1734  L. Euler  He found g = 0.577218. 
15  1736  L. Euler  The EulerMaclaurin summation was used [1].

19  1790  L. Mascheroni  Mascheroni computed 32 decimal places, but only
19 were correct. 
24  1809  J. von Soldner  In a work on the logarithmintegral function.

40  1812  F.B.G. Nicolai  In agreement with Soldner's calculation. 
19  1825  A.M. Legendre  EulerMaclaurin summation was used with n=10
[2]. 
34  1857  Lindman  EulerMaclaurin summation was used with n=100. 
41  1861  Oettinger  EulerMaclaurin summation was used with n=100. 
59  1869  W. Shanks  EulerMaclaurin summation was used with n=1000. 
110  1871  W. Shanks  
263  1878  J.C. Adams  Adams also computed the first 62 Bernoullian
numbers [5]. 
32  1887  T. J. Stieltjes  He used a series based on the zeta function.

???  1952  J.W. Wrench  EulerMaclaurin summation [7]. 
1271  1962  D.E. Knuth  EulerMaclaurin summation [8]. 
3566  1962  D.W. Sweeney  The exponential integral method was used
[9]. 
20,700  1977  R.P. Brent  Brent used Sweeney's approach [10].

30,100  1980  R.P. Brent and E.M. McMillan  The Bessel function method [12] was used 
172,000  1993  J. Borwein  A variant of Brent's method was used. 
1,000,000  1997  T. Papanikolaou  This is the first gamma computation
based on a binary splitting approach. He used a Sun SPARC Ultra, and the
computation took 160 hours. He also proved that if g is rational,
its denominator has at least 242080 decimal digits. 
7,286,255  1998 Dec.  X. Gourdon  Sweeney's method (with N=2^{23} )
with binary splitting was used. The computation took 47 hours on a SGI
R10000 (256 Mo). The verification was done with the value N=2^{23}+1. 
108,000,000  1999 Oct.  X. Gourdon and P. Demichel  Formula (7) was used with a binary splitting process. The program
was from X. Gourdon and Launched by P. Demichel on a HP J5000, 2 processors
PA 8500 (440 Mhz) with 2 Go of memory. 