Polya and Hilbert conjectured long ago that the non trivial zeros of the Riemann zeta function are the oscillation frequencies of a physical system, a result that would lead to a proof of the celebrated Riemann hypothesis. In this talk we shall explain how  this idea can be realized by the spectrum of a Dirac fermion in Rindler spacetime subject to a potential constructed from the prime numbers. This result points towards unexpected connections between Number Theory and Theoretical Physics.