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CD Track Lengths - Answer

The lengths of the tracks are (5, 7, 17, 19), (7, 11, 13, 23) and (7, 13, 17, 23).

None of the track lengths can be 2 because any sum of the three different primes, including 2, would not be prime. Therefore, the track lengths must be chosen from the 13 primes between 3 and 43.

To get the answer, find all three prime combinations whose sum is a small enough prime that another prime (larger than any of the three) can be added to result in a sum of 60 or less.

There are 14 such combinations: (3, 5, 11), (3, 5, 23), (3, 7, 13), (3, 7, 19), (3, 11, 17), (5, 7, 11), (5, 7, 19), (5, 11, 13), (5, 13, 19), (7, 11, 13), (7, 11, 19), (7, 13, 19), (7, 13, 17) and (11, 13, 17).

If you try all possible fourth primes with those combinations, you'll find that the only possibilities which meet the requirements (sum of 60 or less and sum of any three is a prime) are the answers given above.