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Ha, super, thanks for making it.

Check out 431 columns - this yields no obvious persistent patterns.

You sure about that? I see some clear diagonal lines at 431 cols: https://imgur.com/a/rNKjTtr

I think you'll find this to be the case with any prime.

Not really. There are almost always clearly visible diagonals. Try 199, 211, 223, etc.

You're right. I guess then it comes down to how far away from a composite it is.