It is Even, Not quite Odd

Number Theory Level pending

Which is the largest positive even integer which 'cannot' be expressed as the sum of two odd composite numbers?

Eg :

$$10=9+1=7+3=5+5$$. 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.

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