  Let pi(x) denote the number of primes smaller or equal to x. We compare
sqrt{pi}(x) with sqrt{R}(x) and sqrt{li}(x), where R(x) and li(x) are the
Riemann function and the logarithmic integral, respectively. We show a
regularity in the distribution of the natural numbers in terms of a phase
related to sqrt{pi}-sqrt{R} and indicate how li(x) can cross pi(x) for the
first time.
