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Obviously $2,3,5,\ldots$ but I'm not sure for what other numbers does it hold, or if there are infinitely many.

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marked as duplicate by lulu, Servaes, Song, J. M. is not a mathematician, Shaun Mar 15 at 14:05

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    $\begingroup$ Are you talking about only Natural numbers? Otherwise $2=12+(-10)$ or like that. $\endgroup$ – Love Invariants Mar 15 at 10:51
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Any $n\ge 13$, prime or otherwise, is either $8$ or $9$ more than an even number $\ge 4$. Therefore, any such $n$ is a sum of two composite numbers. We can exhaustively check the only primes lacking such an expression are the primes from $2$ to $11$ inclusive, i.e. $5$ of them.

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