If you are painting over the same type of paint then primer is not really needed. You said that the walls are dirty, correct? Then, I would wash the walls then primer and then paint. To wash the walls all you need is a large wet sponge to remove all loose dirt and grime. Let dry and apply the primer. The primer will seal the walls and cover some of the imperfections and will save you on paint, because the walls will absorb less. Make sure you use a quality primer and paint. Ask your salesperson about which primer to use with the paint. If you are just looking for a quick fix then go ahead and paint (no primer/no wash). Good Luck.