Prime-counting function
- Category
- RIEMANN HYPOTHESIS
- Definition
- The function pi(x) that counts the number of primes not exceeding x.
- Math Level
- GENERAL
- Index Excerpt
- pi(x); π(x)
The prime-counting function is the number of prime numbers less than or equal to .
It turns the irregular sequence of primes into a function whose large-scale behaviour can be studied. The Prime Number Theorem describes its broad growth, while RH would sharply constrain the error in prime-counting approximations.
See also: prime number, Prime Number Theorem, logarithmic integral, distribution of primes..