Dean Sam and Castiel are three brothers. Interestingly their current age is prime. What's more interesting that difference between their ages is also prime. How old are they ?

Common Wrong Answers
“1, 3, 5”
While all the ages (1, 3, 5) are prime, the age differences are not all prime. The differences are 2 (which is prime) and 2 (which is prime), but the age of 1 is not a valid age since it implies a non-adult, which doesn't fit the context.
“3, 4, 7”
The ages 3, 4, and 7 include a non-prime age (4), which disqualifies this set. Additionally, the age differences are 4 (not prime) and 3 (prime), failing the prime age difference criteria.
“2, 3, 6”
Although 2 and 3 are prime, 6 is not. Furthermore, the age differences include 4 (6-2) and 3 (6-3), where 4 is not a prime number, which violates the requirements of the riddle.
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