## Task 1 - 110711

Determine all four-digit natural numbers $Z$ with the following properties:

(1) The number $Z$ is divisible by 8.

(2) The digits of $Z$ are pairwise different, i.e., in each of these numbers, each digit may appear at most once.

(3) All used digits represent, individually considered, prime numbers.
Due to (3), only the digits 2, 3, 5, and 7 are possible. Due to (2), all of these digits must be used in each of the sought numbers. Therefore, and due to (1), the digit 2 must occupy the units place of the sought numbers.

Thus, the numbers 3572, 3752, 5372, 5732, 7352, and 7532 can at most meet the conditions of the problem.

The numbers 3752 and 7352 are divisible by 8, while the others are not. Therefore, 3752 and 7352 are the only ones that fulfill all the conditions of the problem.