Asymptotic Harmonic Behavior in the Prime Number Distribution

Maurice H. P. M. van Putten

Sejong University, Seoul, South Korea.

DOI: 10.4236/am.2014.516244                

Abstract

We consider 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 . The first 21 zeros give rise to asymptotic harmonic behavior in Φ(x) defined by the prime numbers up to one trillion.

Keywords

Prime Number Distribution, Summation, Regularization

Conflicts of Interest

The authors declare no conflicts of interest.

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