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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  


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.

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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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