Cîmpeanu Scaling Law: Empirical Verification on 10 Million Primes Reveals Hyperbolic Geometry in Prime Distribution

This repository contains the complete computational verification of the Cîmpeanu Scaling Law in prime number theory. Key Findings:• Scaling law: Δ√p_n ∼ C √((ln p_n)²/p_n) with α = 2• Empirical constant: C = 0.50002283 ± 0.42630578• Theoretical match: 0.5 with 0.004566% relative error• Dataset: 10,000,001 primes (up to 179,424,691)• Statistical validation: p = 0.792, no overfitting detected Contents:1. Untitled55.ipynb - Complete Google Colab verification notebook Methodology: Optimized prime sieve + JIT-accelerated computation in Python/Numba.Significance: Reveals hyperbolic geometry (ds = dp/p) in prime distribution.