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Prime numbers are important in music. They're actually random. Repetition of this randomness makes music beautiful.

2 and 3 are, but that's about where it ends. Yeah you can do subdivisions of 5 and 7 but it starts to be an academic exercise at that point. So, no, prime numbers don't have any special relationship to music, sorry. Factors of 12 and 16 are actually the most common and useful groupings in most music that people can dance to.

On this last point, I recall reading an in-depth article (whose title I've forgotten..) about the importance of highly divisible numbers in music.

12 has a wonderful property of being variously composable by 2, 3, 4, 6 - and one reason why it's so commonly used in music is that it's not a prime number.

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