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Computational Results for Gaussian Moat Problem
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E88-A No.5 pp.1267-1273
Publication Date: 2005/05/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
graph algorithm, Gaussian prime, parallel computing,
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"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 =, whereas the best previous result was k = due to Gethner et al. The amount of computation needed for k = is about 5000 times larger than that for k =. 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.