math 101

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:

Today, March 14th, is Pi day - can you guess why that particular day? We all know Pi = 3.1415..., but what does this quantity represent, ontologically?

I spent a few minutes figuring it out and then I checked Wikipedia which gave me a very good visualization of the meaning of that number:

What that means is that Pi is actually a distance, namely the circumference of a circle whose diameter is one.