3. Determine the largest prime number whose all digits are distinct such that any permutation of its digits yields another prime number.
3. If the desired number is at least two digits, then in its representation, digits from the set $\{0,2,4,5,6,8\}$ must not appear (since by moving such a digit to the end of the number, we would obtain a number that is not prime). Thus, only four possible digits remain: $\{1,3,7,9\}$, so the desired number can be at most four digits. If it were four digits, then each of the digits $1,3,7$, and 9 would appear exactly once, but then by permuting the digits, we could obtain the number 1397, which is divisible by 11 and thus not prime. Similarly, for any possible choice of three out of these four digits, we can find a permutation where we do not get a prime number: $7|371,11| 319,7|791,7| 973$. Therefore, the desired number is at most two digits, and among them, we easily find the largest: it is 97 (it is prime, and by permuting its digits, we obtain the number 79, which is also prime).