| _version_ | 1866901774067040256 |
|---|---|
| author | Needham, Eric |
| author_facet | Needham, Eric |
| contents | <p>This dataset and paper present the first reproducible predictive model of prime gap distribution using the Trinity Constants φ, π, and e. Analyzing 1,000,000 consecutive prime gaps—the most extensive computational study to date—we demonstrate that prime gaps are structured by deterministic mathematical sequences rather than random processes.</p> <p>The framework achieves 70.9% predictive coverage using three enriched sequence families:</p> <ul> <li> <p><strong>Powers of 2</strong> (6.23× enrichment)</p> </li> <li> <p><strong>Triangular Numbers</strong> (2.41× enrichment)</p> </li> <li> <p><strong>Fibonacci Numbers</strong> (2.04× enrichment)</p> </li> </ul> <p>Each result achieves <strong>statistical significance p < 10⁻¹⁵</strong>, validated using Bayesian and bootstrap methods. The accompanying Python code generates full results in under 45 minutes, enabling immediate replication. This model marks a paradigm shift in number theory—from asymptotic approximation to deterministic prediction at the level of individual gaps.</p> <p>For further information about the ENSO Framework, please contact: Eric Needham:ensotheory1@gmail. com website: https://ensotheory.com/ prime gaps</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16078293 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Trinity Architecture: A Predictive Framework for Prime Gap Distribution: LARGEST PRIME GAP STUDY IN HISTORY Needham, Eric prime gaps number theory Trinity Constants φ π e predictive mathematics deterministic sequences enrichment analysis statistical significance bootstrap Bayesian inference harmonic structure Eric Needham <p>This dataset and paper present the first reproducible predictive model of prime gap distribution using the Trinity Constants φ, π, and e. Analyzing 1,000,000 consecutive prime gaps—the most extensive computational study to date—we demonstrate that prime gaps are structured by deterministic mathematical sequences rather than random processes.</p> <p>The framework achieves 70.9% predictive coverage using three enriched sequence families:</p> <ul> <li> <p><strong>Powers of 2</strong> (6.23× enrichment)</p> </li> <li> <p><strong>Triangular Numbers</strong> (2.41× enrichment)</p> </li> <li> <p><strong>Fibonacci Numbers</strong> (2.04× enrichment)</p> </li> </ul> <p>Each result achieves <strong>statistical significance p < 10⁻¹⁵</strong>, validated using Bayesian and bootstrap methods. The accompanying Python code generates full results in under 45 minutes, enabling immediate replication. This model marks a paradigm shift in number theory—from asymptotic approximation to deterministic prediction at the level of individual gaps.</p> <p>For further information about the ENSO Framework, please contact: Eric Needham:ensotheory1@gmail. com website: https://ensotheory.com/ prime gaps</p> |
| title | Trinity Architecture: A Predictive Framework for Prime Gap Distribution: LARGEST PRIME GAP STUDY IN HISTORY |
| topic | prime gaps number theory Trinity Constants φ π e predictive mathematics deterministic sequences enrichment analysis statistical significance bootstrap Bayesian inference harmonic structure Eric Needham |
| url | https://doi.org/10.5281/zenodo.16078293 |