prime counting function
The prime counting function is a non-multiplicative function for any positive real number , denoted as and gives the number of primes not exceeding . It usually takes a positive integer for an argument. The first few values of for are (http://www.research.att.com/ njas/sequences/eisA.cgi?Anum=000720OEIS A000720 ).
The asymptotic behavior of is given by the prime number theorem. This function is closely related with Chebyshev’s functions and .
Title | prime counting function |
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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 |