Chances are that primer will cover it in one coat, then you can use the paint color of your choice. White paint will take many layers. Primer is meant to mute out color, but white paint just lays over the top creating a tint through the paint.Imagine wearing a white T-shirt over a black bra...you can see right through.ook, if the existing paint is latex, and there is no moisture problem, cheap latex primer is the same thing as cheap white paint. 'Ceiling white' is fine for primer.