My gut sense is that this has something to do with visualizing the sieve of Eratosthenes, and nothing more than that. But I'd be happy to hear otherwise.
Other than the sieve of Eratosthenes being a way to compute a finite list of primes I don't see the relationship here. Could you elaborate?
I think the relationship is that the sieve has a natural shape since it's based on ruling out multiples.
Isn’t the sieve’s eventual shape just the list of prime numbers?
I don't intent to be rude, but what does that even mean? Can you explain?
Mostly the "pattern holding up until n^2". I don't know exactly how the groups-of-N factors into all this. Maybe it's nothing and there's no clear relationship.