Legendre's Constant

Author

Eric W. Weisstein
February 16, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Plot

<<Utilities`Typesetting`

With[{step=100},
ListPlot[Table[{n,N[+Log[n]-n/PrimePi[n]]},{n,step,10^6,step}],
PlotStyle->Red,
AxesLabel->TraditionalForm/@{n,Log[n]-InlineFraction[n,PrimePi[n]]},
Joined->True,
Epilog->{{Blue,Line[{{0,#},{10^6,#}}]&[1.08366]}}]]