- Prime number theorem states how often primes occur (approx. how densely they are distributed).
- The Shannon theorem of information entropy gives us a lower bound of how much data is at least required to store some information.
- Prime factorization theorem allows us to uniquely map each positive integer number to a set of prime exponents.
Can these things be combined somehow to create a number system which is on average more efficient, than say for example the binary number system?