General Mathematics

Prime Modular Dynamics Theory (PMDT)

Authors: Michel Monfette
Comments: 14 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

We study the modular dynamics of prime numbers through the families SG(k) = {p ∈ P : kp + 1 ∈ P}. We present extensive computational evidence (up to 100 million Sophie Germain primes) fora modular dynamical structure in SG primes modulo 30. Two fundamental theorems establishthe triangular residue class 11,23,29 and gap constraints. Eight conjectures emerge, includinga novel "least-gap principle" and a harmonic attractor at 60. SG(k) families exhibit distinctphases in entropy/detailed-balance plane, with period-9 resonance and asymmetric sexy orbits.A third grammatical dynamic (G3) classifies all anomalies into three energy regimes. These pat-terns suggest an underlying arithmetic grammar and self-organizing behavior in Sophie Germainprimes.
Category: General Mathematics