  We consider $\Phi(x)=x^{-\frac{1}{4}}\left[1-2\sqrt{x}\Sigma e^{-p^2\pi x}\ln
p\right]$ on $x>0$, where the sum is over all primes $p$. If $\Phi$ is bounded
on $x>0$, then the Riemann hypothesis is true or there are infinitely many
zeros Re~$z_k>\frac{1}{2}$. The first 21 zeros give rise to asymptotic harmonic
behavior in $\Phi(x)$ defined by the prime numbers up to one trillion.
