%0 Journal Article
%T Asymptotic Harmonic Behavior in the Prime Number Distribution
%A Maurice H. P. M. van Putten
%J Applied Mathematics
%P 2547-2557
%@ 2152-7393
%D 2014
%I Scientific Research Publishing
%R 10.4236/am.2014.516244
%X We consider <img src=\"Edit_ac7b1471-9bba-467d-9031-bbc8d5b0b951.bmp\" alt=\"\" /> on <em>x</em> &gt; 0, where the sum is over all primes <em>p</em>. If ¦µ is bounded on<em> x</em> &gt; 0, then the Riemann hypothesis is true or there are infinitely many zeros <img src=\"Edit_53346bbb-e28c-4754-af43-acdae2967922.bmp\" alt=\"\" />. The first 21 zeros give rise to asymptotic harmonic behavior in ¦µ(<em>x</em>) defined by the prime numbers up to one trillion.
%K Prime Number Distribution
%K Summation
%K Regularization
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=49468