Nail Pops and Paint

Hi everyone,

We just moved into a new home and the issue is there are nail pops everywhere. We repaired all the ones in the bedroom by tapping the nail back in and securing the nail with an overlapping screw, spackle and sand. As you can see below we have a ton of patches, my question is can I prime and paint over all this or will it still be visible? I am wondering if I will need to do a skim coat over the whole room?

Thanks
Bill

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