The Goldbach conjecture suggests that every even integer greater than $2$ can be expressed as a sum of two primes. For example:
$$10 = 5+5$$ $$12 = 7+5$$ $$14 = 7+7$$
What is so special about even integers? Can we generalize the conjecture as follows?
Every integer multiple of $n$ greater than $n$ can be expressed as a sum of $n$ primes.
$$15 = 3+5+7$$ $$21 = 7+7+7$$ $$27 = 7+7+13$$
In the above example, I didn't include $24$, because I'm adding the additional restriction that the number is not a multiple of a prime less than $n$.