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%I #5 Oct 01 2013 21:35:27
%S 5,14,46,214,1249,8248,58754,440368,3425308,27411417,224368865,
%T 1870559867,15834598305,135780264894,1177208491861,10304192554496,
%U 90948833260990,808675901493606,7237518062753712,65154265428712141
%N Hardy-Littlewood approximation to the number of twin primes less than 10^n.
%C Another good approximation to the number of twin primes < 10^n is the sum of twin primes < 10^(n/2)/4. For example Pi2(10^16) = 10304185697298.
%C SumPi2(10^8)/4 = 10301443659233 for an error of 0.0000266. However, the Hardy-Littlewood approximation is superior giving an error of -0.000000665.
%F C_2 = 0.660161815846869573927812110014555778432623. Li_2(x) = 2*C_2*integral(t=2..x,dt/log(t)^2)
%o (PARI) Li_2(x) = intnum(t=2,x,2*0.660161815846869573927812110014555778432623/log(t)^2)
%K nonn
%O 1,1
%A _Cino Hilliard_, Nov 22 2008
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