Unique interplay between 21 million supply cap and 210,000 block halvening

Kind of a weird title, but essentially I remember a very interesting explanation in this sub a few years ago. I am unable to find it so thought I’d ask for the information again here.

You might notice the expected amount of blocks per halvening (210,000) is exactly one tenth of 21 million (total supply cap). Supposedly this is not an accident.

As satoshi thought about what to set the difficulty adjustment calculation as, he saw that this decision created trade offs in three areas, total supply, # of expected blocks per halvening, and I think actually the initial block subsidy of 50 BTC would change as well.

Obviously I have no idea what I’m talking about, but I have thought back to this relationship a few times over the years and always wished I could remember this sophisticated mathematical relationship between all these things.

Thanks in advance!

EDIT: I also just remembered it’s somehow relevant that the targeted block time of 10 minutes, is directly related to the fact that 10 times 210,000 is 21,000,000. I really hope I’m not sounding like an idiot here.