Dissertation/Thesis
A Constructive Proof of the Infinitude of Mersenne Primes via Bit Templates in Lucas–Lehmer Sequences
| Title: | A Constructive Proof of the Infinitude of Mersenne Primes via Bit Templates in Lucas–Lehmer Sequences |
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| Authors: | Okuda, Tetsuya |
| Publisher Information: | Zenodo |
| Publication Year: | 2025 |
| Collection: | Zenodo |
| Subject Terms: | Mersenne primes, Lucas-Lehmer test, constructive proof, bit templates, Hamming weight, primality testing, binary automaton |
| Description: | We present a constructive and deterministic proof for the infinitude of Mersenne primes. By analyzing the bit-level structure of the Lucas–Lehmer sequence, we identify a recurring “collapse template” of Hamming weights that guarantees successful primality testing. We show that such a pattern can always be constructed and detected algorithmically, thus proving the existence of infinitely many Mersenne primes. |
| Document Type: | Thesis |
| Language: | unknown |
| Relation: | https://zenodo.org/records/16255004; oai:zenodo.org:16255004; https://doi.org/10.5281/zenodo.16255004 |
| DOI: | 10.5281/zenodo.16255004 |
| Availability: | https://doi.org/10.5281/zenodo.16255004 https://zenodo.org/records/16255004 |
| Rights: | Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode |
| Accession Number: | edsbas.8397A03E |
| Database: | BASE |
| DOI: | 10.5281/zenodo.16255004 |
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