4. 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?
4. Suppose the child's age does not exceed 35 years. Let's list all the prime numbers: $2,3,5,7,11,13,17,19,23$, 29,31. It is clear that the age of the younger child is an odd number. The numbers 29 and 31 also do not fit. Let's find the age of the younger child. He cannot be 1 year old, because $1+8=9$. His age cannot end in 3, because $3+2=5$. This leaves $5,7,11,17$ and 19. Not 7 years old, because $7+2=9$. Not 17 years old, because $17+8=25$. Not 19 years old: $19+2=21$. And not 11: $11+14=25$. Therefore, the younger one is 5 years old. Answer: $5,7,11,13,17$ and 19 years.