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Asymptotic Harmonic Behavior in the Prime Number Distribution

DOI: 10.4236/am.2014.516244, PP. 2547-2557

Keywords: Prime Number Distribution, Summation, Regularization

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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.

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