"There are a finite number of prime numbers that use 2048 or less bit" -- Wade Burchette
Finite yes, but also ENORMOUS.
The number of primes less than x, pi(x), is approximated by x / (log x-1) or more roughly, but more conveniently, x / (log x). For 1024 bits, x = 2^1024 which is about 10^308.
pi( 2^1024) ~= 10^308 / 1024 ~= 10^305. As there are probably only about 10^80 atoms in the universe, give or take a power of 10, no such list can exist, even for primes of 1024 bits. For 2048 bits you'd be looking at > 10^600!
So although you have to use primes (otherwise the encryption wouldn't work), "the finiteness" of the number of primes is not a problem. But I thought it was a reasonable question, so if you do get any downvotes, they weren't from me :-)