prime counting function

The prime counting function p(n) gives the number of primes equal or less than n.

According the Prime Number Theorem ¹⁾, for large n the function is approximated by the logarithmic prime counting approximation.

Better approximations of the function have been found as:

• Riemann prime counting approximation
• Neumann prime counting approximation
  

notes

1) Ash 1971 p. 196.