TITLE:
Asymptotic Harmonic Behavior in the Prime Number Distribution
AUTHORS:
Maurice H. P. M. van Putten
KEYWORDS:
Prime Number Distribution, Summation, Regularization
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.16,
September
4,
2014
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.