If there's a minimum length (the Planck length?) then space is discrete and the measurement bottoms out at some point, it would be infinite if space was continuous and infinitely divisible.

Bingo. There are a finite number of atoms in a coastline therefore there is a finite length. I suspect the calculus to derive it isn't even all that hard.

"There are a finite number of atoms in a coastline"

And atoms do not consist of smaller parts?

There are also a finite number of quarks.

Maybe. So can you meassure it then?

Do quarks even meaningfully have a position "inside" the atom?

"If there's a minimum length (the Planck length?) then space is discrete "

"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. "

(https://www.physlink.com/education/askexperts/ae281.cfm)

This does not say, that space is discrete, it says that our concept of space does not make sense anymore at sizes that small.