I'm still a little bit stuck! I considered it mod 6, and considered cases of 2 mod 6, 4 mod 6, and 0 mod 6, and found a way to express the number as the sum of 25, 27, or 35 with an odd multiple of 3 for numbers greater than 38, and 38 cannot be expressed as the sum of two composite odd numbers and neither than any of the 19 smaller even numbers smaller than 38. I tested that 2, 4, ... 36 all don't work by hand, but how do I know without testing all those numbers. Is there a faster way to do this other than "bashing" all of the 19 smaller numbers?