10.26 A Visual Insight into the Harmonic Frequency of Prime Numbers

Abstract 2: 

This article presents a set of diagrams that provide an insight into Prime Frequencies, or the Harmonic Frequency of Primes as Thomas Mario Kalmar would put it.  It explains how the diagrams are made and how they come together.  The diagrams are intimately wrapped up with Prime Numbers, and provide a visual description of how Prime Numbers occur.  Principally, given a prime number, and assuming all other prime numbers up to that prime number are known, the diagrams will reveal the consequent prime numbers up to the square of the first consequent prime number.  It is uncertain that this is an efficient method of divining primes, or if the diagrams actually add anything new to the Theory of Prime Numbers or Number Theory in general.  However I have every reason to believe the diagrams are unique and are interesting in themselves from a purely visual perspective, although they are most similar in appearance to Sacks’ Spirals.  My hope is that they may pique the curiosity of people interested in Prime Numbers.  The diagrams were discovered by thinking carefully (obsessively) about Discrete Fourier Transforms (DFT) and the famous musical concept of the Circle of Fifths.