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March 31, 2026Open Access

Persistent Conditional Dependency in Consecutive Prime Gaps: A Multi-Scale Statistical Analysis

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Authors

LRLee Rich

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Overview

Analysis reveals persistent conditional dependency in prime gaps, indicating significant statistical structure in their distribution.

Key Points

  • The aim is to investigate the conditional dependency among consecutive normalized prime gaps.
  • Utilized a combination of mutual information estimation and autocorrelation analysis.
  • Computed conditional moments and created residue-class transition matrices.
  • Analyzed data from a sample of 455 million primes up to 10^10.
  • Mutual information at 10^10 reached approximately 0.782 bits, indicating a violation of independence assumptions.
  • Lag-1 autocorrelation measured at ρ₁ = −0.0276, suggesting mean-reversion behavior.
  • Residual-class transitions showed significant χ² value of 1.32 × 10^8, consistent across all scales tested.

Cite This Study

Lee Rich (2026) studied this question.

synapsesocial.com/papers/69cb6556e6a8c024954b97e0https://doi.org/10.5281/zenodo.19323116
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