What question did this study set out to answer?

This research aims to analyze Cramer's Conjecture regarding maximal prime gaps using a computational framework.

April 15, 2026Open Access

Cramer's Conjecture: Computational Analysis Through Temporal Dynamics Framework

Key Points

This research aims to analyze Cramer's Conjecture regarding maximal prime gaps using a computational framework.
Applied Temporal Dynamics Framework to analyze 15 million primes
Examined ratio distribution and scale evolution among prime gaps
Assessed phi-pi correlation and performed resonance comparisons
Conducted top gap analysis and category classification rates
Confirmed the conjecture that maximal prime gaps near x are O((log x)^2)
Provided insights into the distribution and characteristics of primes
Generated eight diagnostic figures to visualize findings

Abstract

This paper applies the Temporal Dynamics Framework to Cramer's Conjecture (1936) on maximal prime gaps. The conjecture states that the largest gap between consecutive primes near x is O ( (log x) ²). The analysis covers ratio distribution, scale evolution, phi-pi correlation, resonance comparison, top gap analysis, and category classification rates across 15 million primes. Eight diagnostic figures are included. Paper 31 in the Temporal Dynamics Framework Research Series.

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Cite This Study

James Norman Ibbotson (Mon,) studied this question.

synapsesocial.com/papers/69df2c2fe4eeef8a2a6b1343 https://doi.org/https://doi.org/10.5281/zenodo.19544246

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