Ok this nerd-sniped me pretty good, never seen this before and assumed it would be quickly connected to the Ulam spiral mentioned elsewhere in the the thread. That particular rabbit hole kinda bottoms out in polynomial residues and the very mysterious-sounding "Conjecture F" [0].

This parallax primes thing though led to the linked page [1] which has lots of background and other connections, including the most satisfying part, which turned out more geometric [2]

[0] https://en.wikipedia.org/wiki/Ulam_spiral#Explanation [1] https://www.novaspivack.com/science/we-have-discovered-a-new... [2] https://www.cut-the-knot.org/Curriculum/Arithmetic/PrimesFro...