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The Gaussian moat problem

Gaussian primes are primes in the integer lattice of complex numbers.

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1 record · How we rate progress

Understanding the problem

Read the background

Gaussian primes are primes in the integer lattice of complex numbers. The moat problem asks whether one can walk forever through distinct Gaussian primes with a fixed maximum step size.

Read the claim in its exact mathematical setting. A manuscript is a research report; its presence in this catalog does not establish that the proof has been independently verified or that the historical novelty assessment is complete.

Why it matters

A focused research target whose precise scope can be followed separately from the general capability of an AI system.

What counts as progress

A sourced new theorem, construction, bound, algorithm, or formalization with its baseline and evidence stated.

What to watch for

  • Check the formal statement, assumptions, and cited prior results against the claimed improvement.
  • Keep author-reported checking, independent checking, and manuscript availability separate.
  • Track revisions to the pinned source and any subsequent expert assessment.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.