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I just came up with this question when I was thinking about the Goldbach conjecture.
For example,
$$2=5 \oplus 7$$
$$4=3 \oplus 7$$
$$6=3 \oplus 5$$
$$8=3 \oplus 11$$
$$10=7 \oplus 13$$
$$12=7 \oplus 11$$
$$14=5 \oplus 11$$
I verified the even numbers up to $10^5$, there weren't any counterexampl...
