prime counting function

The prime counting function is a non-multiplicative function for any positive real number x, denoted as π(x) and gives the number of primes not exceeding x. It usually takes a positive integer n for an argument. The first few values of π(n) for n=1,2,3, are 0,1,2,2,3,3,4,4,4,4,5,5,6,6,6,6,7,7,8,8 ( njas/sequences/eisA.cgi?Anum=000720OEIS A000720 ).

The asymptotic behavior of π(x)x/lnx is given by the prime number theoremMathworldPlanetmath. This function is closely related with Chebyshev’s functions ϑ(x) and ψ(x).

Title prime counting function
Canonical name PrimeCountingFunction
Date of creation 2013-03-22 12:49:00
Last modified on 2013-03-22 12:49:00
Owner XJamRastafire (349)
Last modified by XJamRastafire (349)
Numerical id 13
Author XJamRastafire (349)
Entry type Definition
Classification msc 11A25
Classification msc 11A41
Classification msc 11N05
Related topic LogarithmicIntegral2