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Asymptotic Harmonic Behavior in the Prime Number Distribution

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DOI: 10.4236/am.2014.516244    4,620 Downloads   5,106 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

van Putten, M. (2014) Asymptotic Harmonic Behavior in the Prime Number Distribution. Applied Mathematics, 5, 2547-2557. doi: 10.4236/am.2014.516244.

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