Technically, you only have to prime if you are changing different types of paint. Example, from an oil base paint to a water based paint. Or, if there has been repairs to your walls. If your walls are in good shape and clean, you could go ahead and apply 2 coats of your white paint.
It could take more than two coats if the pink is very bright or your white paint has little or no tint (a bright white). It also depends on the sheen and quality of the paint.