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Claim. E. Gethner and H. M. Stark, Periodic Gaussian moats, Experiment. Math. 6 (1997), no. 4, 289--292. The authors' published summary states the question as whether one can walk from the origin to infinity on the Gaussian primes in steps of bounded length, conjectures that the answer is no from any starting point, and says that the paper introduces periodic Gaussian moats to prove this conjecture for step sizes $\sqrt2$ and $2$. So no infinite sequence of distinct Gaussian primes, starting anywhere, has every step of length at most $2$, and Problem 952 has a negative answer for every step bound $C\le2$. Vardi's survey (card, p. 276) credits the step-$2$ case to Gethner and Stark and the step-$\sqrt2$ case to Jordan and Rabung. The journal record gives the year and no day, so this page carries the first of January.

Covers. No infinite sequence of distinct Gaussian primes has every step of length at most $2$, from any starting point; the question for larger step bounds is not covered.

Depends on. No page of this wiki.

Acceptance. Refereed: Experimental Mathematics 6 (1997). The site labels the problem OPEN, so no curator acceptance is listed. The theorem is stated from the paper's published summary; its proof has not been reproduced here.