Painting hollow doors

Yes, priming is always the first step. Use 2 thin coats of primer.Don't worry if the first coat lets the wood show through. The 2nd coat will fix that. Then use 2 coats of high quality paint. Don't skimp on quality paint and primer. You will be sorry when your paint job doesn't hold up.

I would prime them so I would be certain of a smooth finish.

Prime every paint job you do. Before you prime, remove all hardware, then do a light sanding with a fine grit sandpaper. Use a tack cloth to get rid of all dust and fibers. Let primer dry completely, then paint. Good luck.

i have hollow core doors and I painted them with hi gloss white, two coats, no problem.

yes

It is a good idea to prime anything you are repainting. It helps the finish coat to adhere better.