Stephens' Constant

Author

Eric W. Weisstein
April 16, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/StephensConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/StephensConstant.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Numerical Value

one=SetPrecision[1,25];

(10^5)

ps=Prime[Range[10^5]];//Timing

Times@@(one-#/(#^3-1)&/@ps)//Timing

(10^6)

ps=Prime[Range[10^6]];//Timing

Times@@(one-#/(#^3-1)&/@ps)//Timing

(10^7)

In[1]:= ps = Prime[Range[10^7]]; // Timing
Out[1]= {86.01 Second, Null}

In[3]:= one = SetPrecision[1, 25];

In[4]:= Times @@ (one - #/(#^3 - 1) & /@ ps) // Timing
Out[4]= {286.03 Second, 0.575959969053763007}