Really big numbers are fascinating to me.
For example, private key/address collisions in Bitcoin are theoretically possible, but practically impossible. The number of possible private keys is so mind-bogglingly big!
Discussion
People still run the large bitcoin collider hoping to find key collisions haha.
As an experiment a few years back I set up a server that was just generating private keys 24/7 and checking to see if it already had a balance. I ran it for a month on a pretty fast server and it didn't find anybody's Bitcoin. Even if you put all the computers in the world toward that task you probably wouldn't find any keys that were already in use.
That sounds like a fun experiment for an idle server. I know the LBC "puzzle keys" got solved but people at least knew what address spaces to look in for those so it doesn't really count.