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Comment by CGMthrowaway | Hacker News Reader

Kind of makes me wish that there were recognizable shapes for primes bigger 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) that didn't just look like circles. Because my favorite part about this is how you can see at a glance what the factors are. Except for primes 7 or greater I find myself cheating and looking at the top left for which prime it is.

Is there some non-regular polygon that would be more distinctly recognizable to use for 7, 11, etc?

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I asked somewhere here about the algorithm for the position of the dots and got an answer (can I link directly to a post?) below. Putting things on a circle sounds like a good way to do it but it sort of precludes special arrangement for specific numbers. Not that it could not be done but what would the algorithm look like?

Edit: I looked more at the animation some more and maybe I am wrong. Anyway I may try to make one.

In what is surely not a coincidence, 2012 is also the year in which a Stack Exchange question about how to generate these beautiful diagrams in Mathematica came up: https://mathematica.stackexchange.com/questions/11657/factor...

I wrote an answer there that produced these diagrams from fairly few lines of code.

The question there referred to same now-broken link mentioned above so the origin still unknown.

4 isn’t prime.

You could probably use the binary expansion to group the dots? So, 1 is • 2 is •• 3 is _• •_•

5 is

_• •_• •_•

7 is ____• _•_____• •_•___•_•

11 is ____• _•_____• •_•___•_• •_•___•_•

And so on.

(So, 2n is represented as n next to n, unless n is 2 in which case it is n above n, and 2n+1 is 1 above 2n )

Alternatively, using stars instead of n-gons could also be clearer?

Aren't 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) also "circles" with less resolution? The visualization is just consistent.

Yes I dont disagree and it is elegant as is, but the way our eyes/ brain works it's much harder to ID septagon, nonagon, triacontahenagon etc at a glance. A non-regular shape would be better fit for purpose

Couldn't you draw it in a recognizable way using summation?

7 = 2*3+1

11 = (2*2+1)*2+1

etc...

Interesting idea

Agree. I watched for a while to see some larger primes and was a little disappointed.

Filled polygons would offer some more shapes. Filled hexagon = 7, etc etc...

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