  We present an explicit formula for a weighted sum over the zeros of the
Riemann zeta function. This weighted sum is evaluated in terms of a sum over
the prime numbers, weighted with help of the Hermite polynomials. From the
explicit formula presented in this note, it follows that prime numbers
determine the distribution of the zeros of the Riemann zeta function. In fact,
it is possible to compute the zeros of the zeta function without actually using
this function.
