---

Madhuparna Das, A Note on The Gaussian Moat Problem, arXiv:1908.10392 (v1 27 August 2019, v2 6 September 2024). This page rests on the arXiv record, accessed as the problem page records, not on the paper itself.

The claim. The answer to Problem 952 is no: the abstract says that an infinite sequence of distinct Gaussian primes cannot have its consecutive differences bounded by an absolute constant, stated for the Gaussian primes $p=a^2+b^2$ with $a,b\neq0$, that is, for the primes off the two axes, and that the proof treats each prime $(a,b)$ as a lattice point of the plane and uses the properties of those points. The restriction to primes with both coordinates nonzero is the author's; the question itself admits every Gaussian prime.

Depends on. Nothing in this wiki.

Standing. Withdrawn by its author: version 2 of the arXiv record carries the comment "The claim in Theorem 3 is incorrect. The defined paths P_i (for i=1,2,3,...) do not cover all the Gaussian primes. Additionally, the paths include Gaussian integers, not just primes. Without a proper error term computation, the claim does not hold". The claim was never accepted: the site's page, thread and label never mentioned it, and the search dated 2026-09-18 found no acceptance. The problem's standing is unaffected; the negative answer is proved by the accepted 2026 claim.