  The Riemann hypothesis states that all nontrivial zeros of the zeta function
lie on the critical line $\Re(s)=1/2$. Hilbert and P\'olya suggested a possible
approach to prove it, based on spectral theory. Within this context, some
authors formulated the question: is there a quantum mechanical system related
to the sequence of prime numbers? In this Letter we show that such a sequence
is not zeta regularizable. Therefore, there are no physical systems described
by self-adjoint operators with countably infinite number of degrees of freedom
with spectra given by the sequence of primes numbers.
