Prime factors

Like many people, I am obsessed with prime numbers. To understand more about them, I plotted a 2D diagram of the natural numbers, showing for each the prime factors and where they occur. I was astonished to find obvious regularities that, in hindsight, make sense, but that I had never encountered before.

Here's the diagram, made manually on a spreadsheet. I'd love to hear your observations.

Here are mine:
* Every number repeats as a factor at its own frequency: 2 repeats at every 2 numbers, 3 at every 3 numbers, etc.
* The numbers where no previous frequency repeats are prime numbers.
* Each number starts its own sequence, displayed here as a line with different slope and color. What is the significance of this slope?
* In this 2D space, one octant is enough to represent all numbers and all factorizations.

Other people have thought along the very same lines, independently, and have commented on this post. Bringing more credence simultaneously to the hypotheses of an idea field, as well as that the internet is a mirror to our thoughts.

numbers.png58.69 KB
numbers.ods17.83 KB