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


closed as off-topic by Servaes, Shaun, Alex Provost, dantopa, jgon Mar 15 at 20:39

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Hint $n-8$ and $n-9$ cannot be both prime, if $n \geq 12$.

  • 1
    $\begingroup$ Can you please elaborate? Thank You. $\endgroup$ – Swapnil Das Mar 17 '15 at 4:07
  • 4
    $\begingroup$ I really thought that would enlight instantly. Maybe $n=(n-8)+8=(n-9)+9$ does. $\endgroup$ – MooS Mar 17 '15 at 5:49

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