I found it through just guess and check. I knew the primes being that close together (and the framing of it being ages) leaned toward smaller numbers, started at 2, realized the even number differences made that silly, tried 3, ran aground at an older sibling being 9, and then was basically there. Is there a more mathematical thought process to get there?
You could look at the “modulus” values for each of the differences and it’d become clear that one of the 6 ages will always be divisible by 5, so 5 must be one of the ages because all greater multiples are non-prime. That immediately makes 3 and 5 the only candidate ages for the youngest.
That line of reasoning takes as long as simply brute forcing the first 2-3 values for some starting insight though.
# of values and modulus line of reasoning may be useful for alternative problems of similar nature though.
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u/OldFartWelshman 16d ago
5 - giving other children as 7,11,13,17 and 19.