I think of it just slightly differently -- 256 bytes, 2048 bits -- so 2^2048 (same result as your 256^256).
To give people (who don't spend time with these numbers all the time, I do b/c of cryptography): 2 ^ 256 is on the order of the /number of atoms in the entire universe/ -- every star, moon, comet, black hole, galaxy, etc. across the entire known universe)
Now consider this: 2^512 -- take every single atom in the universe, and imagine that that atom //contains a universe of atoms//. Congratulations, you're only at 2 ^ 512.
I think of it just slightly differently -- 256 bytes, 2048 bits -- so 2^2048 (same result as your 256^256).
To give people (who don't spend time with these numbers all the time, I do b/c of cryptography): 2 ^ 256 is on the order of the /number of atoms in the entire universe/ -- every star, moon, comet, black hole, galaxy, etc. across the entire known universe)
Now consider this: 2^512 -- take every single atom in the universe, and imagine that that atom //contains a universe of atoms//. Congratulations, you're only at 2 ^ 512.
Imagine how large 2 ^ 2048 is!