Computational results for Gaussian moat problem
"Can one walk to infinity on Gaussian primes taking steps of bounded length?" We adopted computational techniques to probe into this open problem. We propose an efficient method to search for the farthest point reachable from the origin, which can be parallelized easily, and have confirmed the existence of a moat of width k = root 36, whereas the best previous result was k = root 26 due to Gethner et al. The amount of computation needed for k = root 36 is about 5000 times larger than that for k = root 26. A refinement of Vardi's estimate for the farthest distance reachable from the origin is proposed. The proposed estimate incorporates discreteness into Vardi's that is based on percolation theory.
gaussian prime graph algorithm parallel computing