Considering a large portion of cryptography is based around large prime numbers being incredibly hard to find, I find it hard to believe anybody has found a significant pattern in them. That’s kind of the whole point.

Can you link to what you’re talking about?

The only thing I can think of is the sieve of Eratothenes, but geometric representations aren’t typical, and they aren’t that pretty of a picture. For the ones I’ve seen, anyway.