The behavior of a function f(n) as the inputs (n) approach infinity / become very large ###### Prime number counting the **prime number theorem** (**PNT**) describes the [asymptotic](https://en.wikipedia.org/wiki/Asymptotic_analysis "Asymptotic analysis") distribution of the [prime numbers](https://en.wikipedia.org/wiki/Prime_number "Prime number") among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. Average gap between consecutive prime numbers among the first N integers is roughly log(_N_)