Periodic Function Approach to Prime Number Analysis with Graphical Illustrations

This paper introduces a novel approach employing periodic functions
for the comprehensive analysis of prime numbers. The method encompasses
primality testing, factor counting and listing, prime distribution
calculation, and the determination of the Nth prime. The exposition of
the technique is presented in a clear and sequential manner, guiding the
reader through each step with explicit equations. Graphs are strategically
incorporated between crucial stages to facilitate a rapid and intuitive visualization
of the rationale and outcomes of each maneuver. The paper
concludes with concise reflections and ongoing inquiries into the potential
applications and refinements of the proposed method.