Can someone elaborate on the relationship of the Riemann zeros and primes? How are the zeros harmonic to the primes? The quotes below mention the 'sum of its complex zeros' and 'other sums over prime numbers'. Can someone clarify this? From Answers.com: "The zeros of the Riemann zeta-function and the prime numbers satisfy a certain duality property, known as the explicit formulae, which shows that in the language of Fourier analysis the zeros of the Riemann zeta-function can be regarded as the harmonic frequencies in the distribution of primes." "In mathematics, the explicit formulae....first case known was for the Riemann zeta function, where sums over its complex zeroes are identified with other sums over prime numbers."