Finite-Scale Markovian Dynamics of Prime Residues and Implications for Quantum Factorization

This technical note provides a rigorous framework for analyzing the distribution of consecutive prime residues modulo 6 The document further explores the information-theoretic implications of this bias, quantifying a measurable entropy deficit in the resulting Markov chain. Finally, a proprietary quantum algorithmic framework is proposed, utilizing the Quantum Fourier Transform (QFT) to exploit latent periodicities within the prime residue sequence. This method aims to provide a novel approach to integer factorization by leveraging intrinsic arithmetic structures rather than modular exponentiation. This document is uploaded to establish intellectual priority and timestamp the conceptual realization of the 'Cîmpeanu-Markov-(confidential)' hybrid approach.