I'm trying to write an algorithm (in Python, if that matters) that prints all the combinations of 5 prime numbers, but I want the first combination to have the lowest sum, the second combination to have the second lowest sum, etc. Is there a way to do this, or approximately do this?

I think the way to do this (broadly) is to find all the combinations for the set (p(1)... p(n)) (where p(n) is a prime), then adding p(n 1) to the set and finding the combinations that I didn't already find, then adding p(n 2) and doing the same thing. I'd really like a solution like this, actually, because I could use a generator function for the prime numbers, so I can just call prime.next() everytime I've exhausted all the possible combinations of n primes.

Thanks for the help, folks. Combinitorics makes my head spin, and any help would be appreciated.