Terence Tao explains the music of the primes.

A talk on primes by Terence Tao. ( Tao won all the prizes there are to give. Charlie Eppes for real? A living Ramanujan? Decide for yourself. )

We start with a "sound wave" that is "noisy" at the prime numbers and silent at other numbers; this is the von Mangoldt function. Then we analyze its notes or frequencies by subjecting it to a process akin to Fourier transform; this is the Mellin transform. Then we prove, and this is the hard part, that certain "notes" cannot occur in this music. This exclusion of certain notes leads to the statement of the prime number theorem. - Tao