Gaussian Moat Cuda

The crown jewel of my explorations lately.

It all started with my GitHub account being blocked for way too many commits (agents overcooked, I guess). So I decided to write a math paper. No one can block the mathematical paper, right?

The thing is - I am an engineer, not a cracked mathematician who can dream proofs. But I have deep respect for the domain of math, and some weird obsession with prime numbers. So I searched for problems where a proper update of infrastructure is due. Problems where a fresh engineering gaze can make things dramatically better. The shortlist ended up being the Busy Beaver problem, ABC triples search, and the Gaussian Moat Problem. The last one clicked the most.

After 5 rounds of trial and error, analytical proofs, and computational dead ends, I arrived at a novel approach: GPU-friendly and roughly 400 times faster on a single 4090 compared to the Pentium II cluster from 2004. In dollar terms, this looks like roughly 15-25k per dollar speedup.

Idea? Simple - GPU talks tiles, problem talks annular bands. Populate the band with tiles.

Status as of May 2026: finalizing computations, polishing the analytical side, and converging to the paper soon. Found a finer upper boundary estimate for the sqrt(36) static-annulus moat around R=72.74M. For sqrt(40), the current 850M-zone result is a hardened static-annulus detector moat at W=262144, R=855000001, with clean BZ, full ingest, and sample audit.

P.S. Used a lot of fun and non-trivial methods. Potential endgame after this problem could be computations for the Riemann Hypothesis. Researching the state there.