ImPerfectHackers proof is quite simple (and neat):

Suppose that there is an integer

not the sum of two composite integers.

Then

is even or odd.

Case 1:

even, put

, then both

and

are even and greater than

and hence composite, but this contradicts our assumption so

cannot be composite.

Case 2:

odd, put

, then both

is composite and

is even and greater than

and hence composite, but this contradicts our assumption so

cannot be composite.

Case 1 and Case 2 together contradict the original assumption and so the theorem: Every integer > 11 is the sum of two composite integers; is proven by contradiction.

RonL