I remember there being an archive that indexed a random stream of numbers from which you could download a range of random bytes, the idea being theoretically everything can be found within the dataset. I think it was done in protest of copyright or something like that.

I can't remember the name of it for the life of me.

Library of babel?

Yep - Vsauce has a nice video here: https://www.youtube.com/watch?v=k1bbInWfAgA

Do monkeys really produce an uniform distribution of keystrokes? Humans don't, and they're also primates.