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Comment by lrossi | Hacker News Reader

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lrossi·

Prime numbers in 2 dimensions. I’ve never thought of this before, but I like the idea.

Interestingly, when plotting them, some patterns appear: https://demonstrations.wolfram.com/GaussianPrimes/

I would have expected patterns due to symmetry around the axes, but there seems to be more than that.

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If you like that, then you'll love this: https://en.wikipedia.org/wiki/Ulam_spiral

Oh cool, thanks for posting this! I used to do that back in school to kill time and later started using it to create drawings by following connect-the-dots rules. We had a get together some time ago (before Covid) where we did communal painting, and one of the rules produced a nice bird-looking thing. :) Great to see there is a name for this sort of thing.

I did! Thanks¡

There are patterns along the coordinate axes and also along the diagonals, but otherwise the distribution looks pretty random: https://commons.wikimedia.org/wiki/File:Gauss-primes-768x768...

And 4 dimensions: See Hurwitz quaternions.

Huh, I'd never heard of that one. I suppose that means that E8 is the equivalent for octonions? That loses the concept of "prime," which is no surprise, because the octonions are not a field, but I wonder if one could bring it back by substituting irreducible representations for primes, somehow? I'm not sure how to carry this off, because I dropped representation theory in grad school, but it seems like an interesting concept to play with, at least.

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