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A086680 Number of primes < 4^n. 1

%I

%S 0,2,6,18,54,172,564,1900,6542,23000,82025,295947,1077871,3957809,

%T 14630843,54400028,203280221,762939111,2874398515,10866266172,

%U 41203088796,156661034233,597116381732,2280998753949,8731188863470

%N Number of primes < 4^n.

%C These numbers approximate the sum of primes < 2^n. The sum of primes < 2^20 = A130739(20) = 41162256126. The number of primes < 2^40 = 41203088796. The error is -0.000991993. From A007053, we have number of primes < 2^74 =375744164937699609596 and sum of primes < 2^37 =375743480734175191581 for an error of -0.0000018209325.

%C Justification sumprimes(n) ~ Pi(n^2) can be found in the link.

%H Cino Hilliard, <a href="http://groups.google.com/group/primes-less-than-x/web/sum-of-primes-less-than-n"> Sum of primes less than n</a> [Cino Hilliard, Feb 13 2009]

%e for n=2, 2,3,5,7,11,13 are the 6 primes < 2^4.

%Y Cf. A007053, A130739.

%K nonn

%O 0,2

%A _Cino Hilliard_, Jul 28 2003

%E Extended by _Cino Hilliard_, Feb 13 2009

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Last modified October 20 21:31 EDT 2021. Contains 348119 sequences. (Running on oeis4.)