Structural Binary Mapping and Mirror Duality in Prime Decomposition: Exact Relations Between MSB, LSB, and Mersenne Numbers
Year: 2026
Type: study-registration
Abstract: This preprint formalizes a matrix-based representation of integers using the total prime factor count $\Omega(n)$ and the prime-counting function $\pi(N)$. Through binary bit extraction, it demonstrates that derived sequences obey strict deterministic laws, generating the complete family of Mersenne numbers and revealing a mirror symmetry between primes and powers of two.
Source: Open Science Framework
Author: José Manuel Briceño Mendoza
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212309536