7.3. In a family, there are six children. Five of them are respectively 2, 6, 8, 12, and 14 years older than the youngest, and the age of each child is a prime number. How old is the youngest?
Answer: $5,7,11,13,17$ and 19

Solution: The remainders from dividing the age differences by 5 are 2, 1, 3, 2, and 4, respectively. Therefore, if the age of the youngest does not divide by 5, then the age of some other child does. Since all numbers are prime, this number is equal to 5. Only the second child fits, otherwise, the age of the youngest would be less than zero. Then the ages are 3, 5, 9, 11, 15, and 17, but not all of these numbers are prime. Therefore, the age of the youngest must be 5. Then there is only one option, and the numbers are $5,7,11,13,17$ and 19.

Criterion: Only the answer - 1 point, a guess that one should look modulo five - plus 1 point. Only one of the cases, when 5 years old is the first or second child, is considered - no more than 4 points.