Prime Number Theorem

= Theorem =

The number of primes less than $$n, \pi (n) \ $$ satisfies

$$\lim_{n \to \infty} \pi(n) \frac {\text{ln}(n)} {n} = 1 \ $$

= Notes =

There are a large number of proofs of the prime number theorem. The first proofs, given independently by Hadamard and Poussin, relied on the theory of functions of a complex variable. Selberg and Erdos would later given elementary proofs of the prime number theorem.

= Proof =