[Grandpa Kim]

Hmm, not quite. It works like this:

pop 100 m 1 fac
pop 200 m 2 fac
pop 300 m 3 fac
pop 400 m 4 fac
pop 500 m 5 fac
pop 1000m 10 fac
pop 2000m 15 fac
pop 4000m 20 fac
pop 8000m 25 fac

If you took advanced storage techniques multiply both pop and fac by 1.2 and round down the facilities.

Some mods give even larger planets and, as i recall, things get even more out of whack.