It is Even, Not quite Odd
Which is the largest positive even integer which 'cannot' be expressed as the sum of two odd composite numbers?
\(10=9+1=7+3=5+5\). In each case, there is at least one number in the sum which is not an odd composite number.
On the other hand, \(24=23+1=11+13=15+9\). In this case, there is a combination of two odd composite numbers.