Can any positive even number be expressed as an XOR of two prime numbers?

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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 counterexamples.

If the Goldbach conjecture is true, how to prove the XOR version?