Asymptotic harmonic behavior in the prime number distribution

We consider $Φ(x)=x^{-\frac{1}{4}}\left[1-2\sqrt{x}Σe^{-p^2πx}\ln p\right]$ on $x>0$, where the sum is over all primes $p$. If $Φ$ 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 $Φ(x)$ defined by the prime numbers up to one trillion.

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