31. Let's call a number complex if it has at least two different prime divisors. Find the largest natural number that cannot be represented as the sum of two complex numbers.
31. The numbers $6, 12, 15$, and 21 are composite and give all possible remainders when divided by 4. Therefore, from any number $n>23$, one of these numbers can be subtracted so that the result is a number of the form $4k+2=2(2k+1)$. Clearly, this difference will be a composite number.