Asymptotic Harmonic Behavior in the Prime Number Distribution


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

Conflicts of Interest

The authors declare no conflicts of interest.


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