10. To enter the castle of Arifmos, you need to enter a code: write down in ascending order the first 10 prime numbers of the natural series, each once. In the resulting multi-digit number, without rearranging the digits, cross out half of the digits so that the remaining ones express: a) the smallest possible number; b) the largest. Find these numbers.
10. Writing down the specified prime numbers, we get 2357111317192329. Since this number has 16 digits, we need to leave 8.

a) To get the smallest number, we need to keep the smallest single-digit numbers on the left. These are the ones. Therefore, we need to remove $2,3,5,7,3,7,9$, and also the eighth digit 3. As a result, we get 11111229.

b) To get the largest number, we need to keep the largest possible single-digit numbers on the left. Since there are 11 digits before the digit 9, the leftmost digit cannot be the remaining digit 9. Therefore, we exclude the digits 2, 3, 5, 1, 1, 1, 3, 1, and the remaining number is 77192329.