On: A visualization of the prime factors of the first ...

[frayesto]

There's a lot of interesting structure. Does this suggest some kind of structure to the space of prime factors or is it just trying to attach meaning where none exists?

[thaumasiotes → frayesto]

Prime factors are defined by a pretty rigid structure; you see a factor of 2 every two numbers; a factor of 3 every three numbers; a factor of 5 every five numbers...

[algorias → thaumasiotes]

For extra fun, if you plot the number of times a specific prime factor occurs, you get a fractal pattern. E.g. for the prime factor 2:

  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
  0  1  0  2  0  1  0  3  0  1  0  2  0  1  0

[thraway180306 → frayesto]

structure to the space of prime factors

There is topological structure https://math.stackexchange.com/questions/2879/mapping-natura... http://ncatlab.org/nlab/show/arithmetic+topology as well as geometric (arithmetic geometry). Question is how does the picture correspond to any of it. Glancing at the UMAP paper https://arxiv.org/abs/1802.03426 it looks like a proper invariant preserving embedding, so maybe loops in the image are real. Even if not, it does hint artistically at sorts of stuff that exist.

[vesinisa → frayesto]

Given that there is definitive visual structure to primes themselves[1], it would be rather surprising if prime factorization had none.

[1] https://en.wikipedia.org/wiki/Ulam_spiral

[tess0r → vesinisa]

Ulam sprials are super interesting. I developed a visualization (and some explanation) once just to understand the problem a little better. Maybe this sparks some interest in someone :)

https://tessi.github.io/walking-the-ulam-spiral/

[jwilk → vesinisa]

On HN 3 months ago:

https://news.ycombinator.com/item?id=17019533

[adamtulinius → frayesto]

"A very pretty structure emerges; this might be spurious in that it captures more about the layout algorithm than any “true” structure of numbers."