Paint doesn't cover them reliably.
If they are really just pinhole size, I'd get a small container of spackle and use your finger to apply a little, then come back just a minute later and wipe the excess off with a just-damp sponge. What you are trying to do is fill a very small hole, but not let the spackle level the "orange peel" effect that the original drywall primer created. Otherwise, the "fix" stands out more than the original hole did.
It should take you minutes.
From holding up pictures.