title: Number of distinct prime partitions
body: <blockquote>
    <p><strong>Possible Duplicate:</strong><br>
    <a href="https://stackoverflow.com/questions/14218882/a-number-as-its-prime-number-parts">A number as it’s prime number parts</a>  </p>
  </blockquote>
  
  
  
  <p>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):</p>
  
  <ul>
  <li>5 + 2</li>
  <li>2 + 5</li>
  <li>3 + 2 + 2</li>
  <li>2 + 3 + 2</li>
  <li>2 + 2 + 3</li>
  </ul>
  
  <p>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.</p>
  
  <p>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.</p>
  
  <p>The highest inputted number is 100.
  Also, the running time of the program cannot exceed 1 second, and the memory limit is 128 MB.</p>