A Hybrid Approach to Prime Gap Distribution: Connecting Finite Computations with Asymptotic Theory

Hybrid computational analysis of prime gaps larger than p_n^alpha. I analyzed 100 million primes to study when g_n > p_n^alpha. Key results: (1) Only 6 gaps exceed sqrt(p_n), all with p_n sqrt(p_n) equals 6/N. (4) No gaps violate the Baker-Harman-Pintz bound (alpha=0.525) for p_n > 31. My hybrid approach connects finite computations with asymptotic theory, providing new insights into prime gap distribution. Complete Python code, Google Colab notebook, and all data included for reproducibility.