Brun's Constant

Author

Eric W. Weisstein
April 16, 2004

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

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

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

Twin Primes

l=Select[Partition[Table[Prime[n],{n,100}],2,1],Subtract@@#==-2&]

Plus@@(1/N[Flatten[Select[Partition[Prime[Range[10^5]],2,1],Subtract@@#==-2&]],20])//Timing

Plus@@(1/N[Flatten[Select[Partition[Prime[Range[10^6]],2,1],Subtract@@#==-2&]],20])//Timing

Plus@@(1/N[Flatten[Select[Partition[Prime[Range[5 10^6]],2,1],Subtract@@#==-2&]],20])//Timing

Once thought to be close to π

1+1/3+1.90195