A Finite-Depth Structural Interpretation of Mersenne Numbers: Exponent Towers, Dominance Constraints, and the GOT–PSM Framework
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| Natura: | Recurso digital |
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2025
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| _version_ | 1866901619124207616 |
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| author | Matsuura, Yoshihito |
| author_facet | Matsuura, Yoshihito |
| contents | <p>This preprint presents a structural and organizational interpretation<br>of Mersenne numbers M_p = 2^p − 1.</p> <p>The purpose of this work is not to propose a new primality test,<br>nor to address infinitude, existence, or density questions<br>concerning Mersenne primes.<br>Instead, the paper restricts a previously introduced<br>finite-depth hierarchical framework—the Global Odd Tower (GOT)—<br>to the domain of prime exponents.</p> <p>Classical results, including divisor congruence conditions<br>and the Lucas–Lehmer test, are reinterpreted<br>as dominance relations and finite-depth verification mechanisms<br>within a unified structural framework.</p> <p>This preprint is intended for subsequent submission<br>to a peer-reviewed journal.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18101023 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Finite-Depth Structural Interpretation of Mersenne Numbers: Exponent Towers, Dominance Constraints, and the GOT–PSM Framework Matsuura, Yoshihito Mersenne numbers structural number theory finite-depth hierarchy prime exponents Lucas–Lehmer test Global Odd Tower Prime Structural Map <p>This preprint presents a structural and organizational interpretation<br>of Mersenne numbers M_p = 2^p − 1.</p> <p>The purpose of this work is not to propose a new primality test,<br>nor to address infinitude, existence, or density questions<br>concerning Mersenne primes.<br>Instead, the paper restricts a previously introduced<br>finite-depth hierarchical framework—the Global Odd Tower (GOT)—<br>to the domain of prime exponents.</p> <p>Classical results, including divisor congruence conditions<br>and the Lucas–Lehmer test, are reinterpreted<br>as dominance relations and finite-depth verification mechanisms<br>within a unified structural framework.</p> <p>This preprint is intended for subsequent submission<br>to a peer-reviewed journal.</p> |
| title | A Finite-Depth Structural Interpretation of Mersenne Numbers: Exponent Towers, Dominance Constraints, and the GOT–PSM Framework |
| topic | Mersenne numbers structural number theory finite-depth hierarchy prime exponents Lucas–Lehmer test Global Odd Tower Prime Structural Map |
| url | https://doi.org/10.5281/zenodo.18101023 |