[Math] Find all even natural numbers which can be written as a sum of two odd composite numbers.

Question

Find all even natural numbers which can be written as a sum of two odd composite numbers.

Please help in in solving the above problem.

Answer 1

Let $n\geq 100$ an even number. Consider the quantities $n-91$, $n-93$ and $n-95$, one of these is a multiple of 3, and not exactly 3 cause $100-95>3$, then is a composite odd number. Observing thet 91,93 and 95 are composite, you conclude that every $n\geq 100$ works. Now check directly the remaining numbers, and you have the solution.