I don't have a very strong math background, but it seems to me self-evident that the strong vertical striping, for instance, would be a trivial artefact of the

I don't have a very strong math background, but it seems to me self-evident that the strong vertical striping, for instance, would be a trivial artefact of the modulus rather than anything interesting about the prime numbers themselves. This leads me to suspect that the rest of the linear striping has a similar explanation which is simply less obvious to me. This in turn leads me to wonder what it is, exactly, that we're looking at. There will always be patterns visible because there is a deep connection between the ability to form a pattern and not-being-a-prime-number; the latter always implies the former, if not the other way around. So how does one perceive a "subtle" pattern of primes when not-being-a-prime is a property possessed by an overlay of an infinite number of patterns?