Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity

This arXiv preprint proposes sieve-based methods, including a concept it calls “reverse sieving,” for studying Gilbreath’s conjecture, an unsolved prime-number problem first posed in 1878. The abstract claims several new results with proofs and a concrete route toward a full solution, while discussing magic primes, forbidden prime constellations, cellular automata, and reductions among equivalent sequences. It also suggests applications to randomness testing, fraud detection, cybersecurity, synthetic data, sequence normalization, and identifying a proposed form of chaos in time series, including Brownian motion. These claims require verification against the paper’s detailed proofs and independent review.