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# All primes

## Question

We are 3 sisters,
today our ages are primes,
interestingly the difference of our ages are also primes.
How old we are ?

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2 5 and 7

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Spoiler

Given that the ages are primes, at least two of the ages must be odd. The difference of any two odd numbers must be even, and as the difference is given to be prime that difference must be 2 -- the only even prime. As the ages must be different (as zero is not prime), it can be deduced that one and only one of the ages must be even, id est 2.  The set of ages must then be {2, p, p+2}, such that p is a prime and p-2 and p+2 are also prime. This only occurs where p is equal to 5: (p-2) = 3 & (p+2) = 7. It therefore can be declared the set of ages is {2, 5, 7}.

Edited by DejMar
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They could be 1, 3 and 5 or 7, 9 and 11. Nice one Jasen!

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Just now, telesphorelalancette said:

They could be 1, 3 and 5 or 7, 9 and 11. Nice one Jasen!

wrong

Spoiler

only 1 answer,  2,5, 7 no more

5 - 1 = 4, not prime

11 - 7 = 4, not prime

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