Prime Analysis: Expressing Primes As Triangles

Prime Numbers have been a hot topic around mathematics for centuries. Many theories have been devised such as the Riemann Hypothesis, Twin Prime Conjecture, etc. However, prime theories involve using many advanced concepts such as the imaginary number and contour integration making it hard for the layman to understand a pattern in primes. Therefore, I propose a theory where comparing the graph of prime against prime roots can help better understand the patterns in primes such as spacing and clustering. Though primes seem random I believe they can be expressed using basic geometric principles. All in all, this research investigates a novel geometric framework utilizing coordinate-based triangular networks formed by prime values and their square roots. By analyzing the asymptotic behavior of the resulting interior angles, this study aims to quantify prime sparsity and local clustering distributions, with the final objective of deriving an alternative geometric expression for prime number distribution standing for the first 500 primes.