Number Theory

    

Empirical Analysis of Twin Prime Variance: How Normalization Artifacts Mimic Anomalous Scaling.

Authors: Bube Ibekwe

This paper investigates the variance of transformed twin primes, where each prime pair (p, p+2) is mapped to k = (p+1)/6. Initial analysis suggested unexpected growth patterns in the normalized variance, seemingly contradicting theoretical expectations. Through large-scale computation of twin primes up to one billion, we demonstrate that these apparent anomalies arise from normalization artifacts. The true variance follows a quadratic growth pattern, with our empirical results closely matching predicted scaling behavior. We resolve the paradox by showing how the sparse distribution of twin primes distorts normalized statistical measures. Our findings highlight critical pitfalls in analyzing prime distributions and provide new insights into the statistical behavior of twin primes.

Comments: 6 Pages.

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Submission history

[v1] 2025-05-17 00:55:57
[v2] 2025-05-22 16:12:15

Unique-IP document downloads: 275 times

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