MATHEMATICAL ENGINEERING TECHNICAL REPORTS Computational Results for Gaussian Moat Problem
نویسنده
چکیده
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 = √ 36, whereas the best previous result was k = √ 26 due to Gethner et al. 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.
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