14. The largest even number that cannot be expressed as the sum of two odd composite numbers is what?

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First, we prove: If $\mathrm{k} \geqslant 40, \mathrm{k}$ is an even number, then $\mathrm{k}$ can be expressed as the sum of two odd composite numbers. For this, if $\mathrm{n}$ is an odd number greater than 1, then $5 \mathrm{n}$ is an odd composite number with a units digit of 5. To express even numbers greater than 40 as the sum of two odd composite numbers, it is only necessary to find some smaller odd composite numbers with units digits of 5, 7, 9, 1, 3, and add them to odd composite numbers of the form $5 \mathrm{n}$. It is easy to see that 15, 27, 9, 21, 33 are such odd composite numbers.

In the following cases, odd numbers $\mathrm{n}>1$ can always be found such that even numbers not less than 40 can be expressed as the sum of two odd composite numbers.
If the units digit of $\mathrm{k}$ is 0 (i.e., 40, 50,
60, ...), then $k=15+5 n$;
If the units digit of $\mathrm{k}$ is 2 (i.e., 42, 52,
62, ...), then $k=27+5 n_{3}$
If the units digit of $\mathrm{k}$ is 4 (i.e., 44, 54,
64, ...), then $k=9+5 n$;
If the units digit of $\mathrm{k}$ is 6 (i.e., 46, 56, 66,
...), then $\mathrm{k}=21+5 \mathrm{n}_{3}$
If the units digit of $\mathrm{k}$ is 8 (i.e., 48, 58,
68, ...), then $\mathrm{k}=33+5 n$.
Therefore, the largest even number that cannot be written as the sum of two odd composite numbers might be 38. Upon inspection, 38 indeed meets this requirement.