Euclid–Euler Theorem and the Largest Known Mersenne Prime: 2^136,279,841 − 1 with 41,024,320 digits — E8 Intelligence Research

FINDING: Euclid–Euler theorem linking even perfect numbers to Mersenne primes, and the discovery of the largest known Mersenne prime \(2^{136\,279\,841}-1\) with 41,024,320 digits. | MATH: \(P = 2^{p-1}(2^{p}-1)\) where \(2^{p}-1\) is prime (Mersenne prime); largest known \(p=136\,279\,841\). | CONNECTION: No direct geometric harmony ratios appear; the structure is purely arithmetic. | DEPTH: 8 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-07
DOI
https://doi.org/10.5281/zenodo.24029679
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Euclid–Euler Theorem and the Largest Known Mersenne Prime: 2^136,279,841 − 1 with 41,024,320 digits — E8 Intelligence Research

Andrew Stewart Caldin
11 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Euclid–Euler Theorem and the Largest Known Mersenne Prime: 2^136,279,841 − 1 with 41,024,320 digits — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Euclid–Euler theorem linking even perfect numbers to Mersenne primes, and the discovery of the largest known Mersenne prime \(2^{136\,279\,841}-1\) with 41,024,320 digits. | MATH: \(P = 2^{p-1}(2^{p}-1)\) where \(2^{p}-1\) is prime (Mersenne prime); largest known \(p=136\,279\,841\). | CONNECTION: No direct geometric harmony ratios appear; the structure is purely arithmetic. | DEPTH: 8 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Euclid–Euler Theorem and the Largest Known Mersenne Prime: 2^136,279,841 − 1 with 41,024,320 digits — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS