The Critical Resonance Band Theory for Mersenne Prime Exponents

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Jose Manuel Briceno Mendoza
DOI: 10.5281/zenodo.18529540
Cited by: 0

Abstract

We have discovered that all known Mersenne prime exponents share a precise "resonance" signature, measured via a function built from fundamental constants. Every known exponent falls within the same narrow numerical band (0.99 to just below 1), revealing a hidden pattern behind these special primes. The theory acts as a predictive filter, identifying new candidate exponents and offering a fresh mathematical perspective on Mersenne prime distribution.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Theories and Applications Advanced Mathematical Theories

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
9 February 2026
Language
EN
Document type
Preprint