  We present a smooth version of Landaus explicit formula for the von Mangoldt
arithmetical function. Assuming the validity of the Riemann hypothesis, we show
that in order to determine whether a natural number is a prime number, it is
sufficient to know the location of a number of non trivial zeros of the Riemann
zeta function. Next we use Heisenbergs inequality to support the conjecture
that this number of zeros cannot be essentially diminished
