Really Hard Math Puzzles

CD Track Lengths

The latest release the group Prime Players Three consists of three CDs. Each has a different playing time. Each CD has four tracts and a total playing time of not more that one hour. The four tracks on any one of these CDs each last a prime number of minutes and each one is a different length. Any combination of the three different tracks on any one of the CDs plays for a prime number of minutes.

What are the lengths in minutes of the track on these three CDs?

Thank you Andrew Gibbons (New Scientist)

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