Prime Discovery Engine

We built a fully portable, GPU-accelerated number theory engine using OpenCL that runs seamlessly on Intel, AMD, and NVIDIA hardware. Our implementation integrates wheel factorization (mod 30, skipping 73% of numbers), Montgomery multiplication for fast modular arithmetic, batch GCD pre-sieving to eliminate 95% of composites, and Cunningham chain detection with mathematical modular filters. The system discovers record-breaking prime gaps, Cunningham chains of both kinds (p→2p±1), prime k-tuples (triplets/quadruplets), and arithmetic progressions in real-time. We visualize discoveries through a live dashboard featuring Ulam spirals, Chebyshev bias counters, gap histograms with Gumbel distribution overlay, and Cramér's conjecture curve. This project helps AMD by demonstrating ROCm/OpenCL's superiority for pure mathematics, providing a compelling case study against NVIDIA CUDA for cryptography, defense, and scientific computing markets.