https://youtube.com/watch?v=sbjPwyPT1AI

Just search www.youtube.com for "numbers theory geometrical". It was posted by "adaycalledzero".

It is a beautiful construction of the prime numbers using a triangular grid, which I have never seen before. The author is someone named Javier Torres Suarez (Alicante, c. 2006). I don't know if it is published in any official journal.

I am still trying to figure out why it works. It is possibly related to Pascal's Triangle or the Sieve of Erastothenes. It also reminds me of the book "A New Kind of Science" by Stephen Wolfram, in which he shows how a cellular automata can generate the prime integers.

While I understand the basic construction process (not why it works), I don't understand which triangles correspond to the prime factors of a given integer. Could you explain how that works?

Rather the latter, embodied into "paper" folding. Each time you fold you create multiples of the factors on a base of the triangle. By the construction or inductively, these are related to the side length of the triangle.

It's a nice piece that I did not see before. I think of writing an illustrative applet.