If this were true, that would provide a way to seemingly compress any number (with the exception of prime numbers, though even those could be compressed by repr

If this were true, that would provide a way to seemingly compress any number (with the exception of prime numbers, though even those could be compressed by representing them as their index in the list of all prime numbers!). The problem is that there can't be a way to compress every number: there aren't enough N-1 bit numbers to compress N bit numbers into (since the former set is only half as big as the latter).