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Number of distinct prime partitions

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Hello. I have this homework assignment of mine, hard as hell, where I have to get all the distinct prime partitions of a given number. For example, number 7 has five different prime partitions (or five different ways of representing the 2 prime partitions it has):

  • 5 + 2
  • 2 + 5
  • 3 + 2 + 2
  • 2 + 3 + 2
  • 2 + 2 + 3


As you can see, the number itself is excluded in the case it's a prime. I don't have to print all the distinct partitions, only the number of them.

So I'm a bit lost with this. I've been completely unable to produce any code, but I think I should approach this from a dynamic programming kind of view. I'm only asking for some hints. Has anyone got an idea? Thanks in advance.

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