Are These Ceiling Stains From Cigarette Smoke?
My grand parents smoked in there home for years, when my grandfather passed we painted the house so my grandmother could sell it, a long story short washing with tsp trisodium phosphate, and painting the brown tar made it through the paint 3x coated we ended up repainting with a schellac based sealer then repainting this finally solved the bleed through problem. You will want to seal the surface not just prime zinsser makes one that I have used since then many times with no bleed through.