logarithmic prime counting approximation
||last updated: 2003-07-20
function approximates the prime counting function.
The first order approximation (a=0) follows from the Prime Number Theorem,
which has been suggested by Friedrich Gauss.
In 1808 Legendre found that for a = 1.08366 the formula gives an even
better approximation for the prime counting.
In 2003 Roberto Neumann found a
variant on this function that approximates the prime counting even better, with
the Neumann prime counting
where the values of the square roots are rounded before using them in the
A comparison of these approximations can be found at www.c-eagle.com.