Prove that every integer n≥12 is the sum of two composites.

Question

Prove that any natural number greater than or equal to 12 is the sum of two composite numbers.

Answer 1

If $n$ is even, then $n$ is the sum of $4$, which is composite, and $n-4$, which is even (a multiple of 2), hence composite, provided $n>6$.

If $n$ is odd, then $n$ is the sum of $9$, which is composite, and $n-9$, which is even (a multiple of 2), hence composite, provided $n>11.$