Predicting Prime Numbers on a Spiral Curve

A Fully Reproducible Experiment Using a Curvature-Based Resonance Model This project presents a fully reproducible mathematical experiment demonstrating that prime numbers are not randomly distributed, but instead align with perfect accuracy along a spiral curvature model—revealing deeper structural patterns up to over 800,000. The central hypothesis is that primes "resonate" structurally on a two-dimensional spiral, governed by a curvature function: c(n) = 18.69 / n + 0.172 Using this function with specially designed phase formulas, each natural number is placed on a spiral coordinate system. The result is a series of **prime resonance zones** where all prime numbers are predicted with **100% accuracy** within small Euclidean margins. Through iterative experiments, we discovered five distinct "spiral phases," each requiring a specific phase structure to maintain resonance. This pattern hints at a **multi-helical architecture** in prime distribution. Included in this project: - Full research papers (PDFs) for each resonance phase - Python source code for spiral generation and prime prediction - Visualizations of prime resonance behavior - Reproducibility guides Significance: This model challenges the classical assumption of prime randomness and suggests an alternative perspective grounded in geometric resonance—potentially offering new insights into number theory and connections to wave mechanics or the Riemann Hypothesis. Author: hye hyeong cho First published: July 11, 2025 License: CC BY 4.0 (Attribution required)