[stargroup100]

Your solution is too linear. You should take into consideration the possible case that immediately adding the largest possible number won't optimize the overall total.

It's possible there is a different combination of the primes that rounds out to a better sum. I recommend this method:

- Separate primes into 3 categories: between 2 and sqrt(n), between sqrt(n) and n/2, and the others
- Add up all of the primes in the last category. These don't change.
- The terms in the second category have the most room for possible optimizations, and therefore should try to be optimized first. They obviously cannot be paired with a prime from its own category, so pair it with a prime from the first category. Try every combination here.
- The last possible case is that 2 primes from the first category might be paired together. Consider this generalization last.

Do it this way and see if you can get to 1356.


NOTE: I'm not sure if the last step is necessary, I'm trying to see if I can prove whether or not that last step is needed.