Heath-Brown–Moroz Constant

Author

Eric W. Weisstein
September 14, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Heath-Brown-MorozConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Heath-Brown-MorozConstant.html.

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

Value

Times@@((((1`20-(1/(#))))^7)(1+((7#+1)/((#)^2)))&[Prime[Range[10^4]]])//Timing

Times@@((((1`20-(1/(#))))^7)(1+((7#+1)/((#)^2)))&[Prime[Range[10^5]]])//Timing

Times@@((((1`20-(1/(#))))^7)(1+((7#+1)/((#)^2)))&[Prime[Range[10^6]]])//Timing

Product[(((1-(1/p)))^7)(1+((7p+1)/(p^2)))/.p->Prime[n],{n,10^4}]//N//Timing

Product[(((1-(1/p)))^7)(1+((7p+1)/(p^2)))/.p->Prime[n],{n,∞}]