Below, m is over 6 million, shown to be accurate, digits of the MRB constant.
In[]:=
m
Out[]=
In[]:=
prec=1010;T=Floor[Log2[prec]];m-Re[INIntegrate[Csc[Pix](E^N[Log[x]/x,prec]-1),{x,1,InfinityI},WorkingPrecisionprec,Method"Trapezoidal"]]//Quiet//AbsoluteTiming
Out[]=
{1.78413,2.2×}
-1009
10
In[]:=
prec=2010;m-Re[INIntegrate[Csc[Pix](E^N[Log[x]/x,prec]-1),{x,1,InfinityI},WorkingPrecisionprec,Method"Trapezoidal",MaxRecursionFloor[Log2[prec]]]]//Quiet//AbsoluteTiming
Out[]=
{12.0038,2.4×}
-2009
10
In[]:=
prec=3010;m-Re[INIntegrate[Csc[Pix](E^N[Log[x]/x,prec]-1),{x,1,InfinityI},WorkingPrecisionprec,Method"Trapezoidal",MaxRecursionFloor[Log2[prec]]]]//Quiet//AbsoluteTiming
Out[]=
{51.4981,5.9×}
-3009
10
In[]:=
prec=4010;m-Re[INIntegrate[Csc[Pix](E^(Log[x]/x)-1),{x,1,InfinityI},WorkingPrecisionprec,Method"Trapezoidal",MaxRecursionFloor[Log2[prec]]]]//Quiet//AbsoluteTiming
Out[]=
{90.6552,3.1×}
-4009
10
In[]:=
prec=5010;m-Re[INIntegrate[Csc[Pix](E^(Log[x]/x)-1),{x,1,InfinityI},WorkingPrecisionprec,Method"Trapezoidal",MaxRecursionFloor[Log2[prec]]]]//Quiet//AbsoluteTiming
Out[]=
{274.296,3.0×}
-5009
10
In[]:=
prec=10010;m-Re[INIntegrate[Csc[Pix](E^(Log[x]/x)-1),{x,1,InfinityI},WorkingPrecisionprec,Method"Trapezoidal",MaxRecursionFloor[Log2[prec]]]]//Quiet//AbsoluteTiming
Out[]=
{2147.41,3.8×}
-10009
10