I always feel it is best to prime again. The primer will soak into the texture and give you a solid surface for topcoating. If you don't prime, you will end up with blotchy areas and dead spots as the paint soaks into the texture unevenly.
Come on, once you are in the mood, how long will putting a nice primer and base for everything else on top take you? And how often are you going to have to suffer this extraordinary pain?
Prime everything again. Then apply two coats of nice finish. Tint the primer if applying a dark color. Then let the kids, dogs, cats, wife and all back in and not worry about it for years or until you tire of the color.
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