## Every Number 40 or Bigger Can be Written as the Sum of Two Composite Numbers

Every even integer from 40 onwards can be expressed as the sum of two odd composite numbers.

Proof

We can write all the even integers in one of the forms

\[10k, \; 10k+2, \; 10k+4, \; 10k+6, \; 10k+8\]

. We can write each of these as the sum of two composite numbers\[10k=15+(10k-15)\]

\[10k+2=27+(10k-25)\]

\[10k+4=9+(10k-5)\]

\[10k+6=21+(10k-15)\]

\[10k+8=33+(10k-25)\]

Take

\[k \ge 4\]

then each term is composite.