The Riemann hypothesis can be interpreted as stating that the prime numbers contain 'music', whose component frequencies are the Riemann zeros.  The question "Frequencies of what?" leads to tantalizing connections with the energy levels of quantum systems whose corresponding classical motion is chaotic.  At the level of statistics, predictions for the Riemann zeros based on semiclassical quantum asymptotics (with primes as periods of classical trajectories) have reached a high degree of accuracy and refinement.  For the zeros themselves, the Riemann-Siegel formula and its improvements lead to new ways of calculating quantum levels.