+6250 I'd write all the numbers less than 20 that can be written as the sum of two primes.
Then sum all the rest. Note that one prime is not the sum of two primes.
2,3,5,7,11,13,17 are the primes of interest
5, 7, 9, 13, 15, 19 are sums including 2
8, 10, 14, 16, 20 include 3
12, 16, 18 include 5
18, 20
and that's it. That leaves
1, 2, 3, 4, 6, 11, 17
These sum to 34
You were on the right track. You just didn't see it through.
Answer: 34
