V- A Constraint-Matrix Formulation of the Twin-Prime Candidate Problem

Key Points

• The aim is to present a structured method for organizing twin-prime candidates using a constraint matrix.
• Introduced a modular 'gate' representation for candidates based on multiples of six.
• Developed a candidate-indexing scheme that utilizes periodic eliminations by small prime divisors.
• Outlined a generalization from twin primes to prime constellations using wheel-gated sieving.
• Provides a compact representation of sieve-style filtering for twin-prime candidates.
• Presents a 2D/3D visualization for tracking candidate survival.
• Establishes a foundation for future computational experiments and optimizations.

Abstract