## The Prime Number Theorem

Euler was aware of the connection between the zeta function

and the sequence of prime numbers 2, 3, 5, 7,...

To see this notices that

so that

and similarly +...

Continuing indefinitely we have

so that

Euler was aware of the connection between the zeta function

and the sequence of prime numbers 2, 3, 5, 7,...

To see this notices that

so that

and similarly +...

Continuing indefinitely we have

so that