Langbehn's Quantum Arithmetic, By Gear to Infinity

The Langbehn Quantum Arithmetic introduces a novel mathematical model for identifying, filtering, and encoding prime numbers using modular arithmetic, lemniscatic spiral structures, and quantum logic. The model is built upon a Modulo-6 system that isolates prime can didates via filter axes (e.g., mod 5, 7, 11), vector-based field resonances, and the generating function x=3(2n−1)±2. Prime numbers are interpreted as stable resonance states in a holographic numerical field, projected through spiral-based transformations and lemniscantic feedback. This system enables arithmetic logic that is suitable for quantum registers, non-classical coding structures, and information topology. By unifying modular sieve theory, topological recurrence, and self-referential encoding (IchBin moments), this model establishes a consistent framework for quantum-compatible arithmetic processing with potential applications in number theory, information physics, and quantum algorithm design.