haven't worked this (don't play a lot of prokofiev myself, though like some of his pieces).
here is what i believe you are referring to. not my fingering, from a reference copy i have from a collection of sonatas and pieces a pianist i'm familiar with worked out. generally i agree with his logic and suggestion but of course you'll need to see if they work.
i personally seldom use anyone's or any editions suggested fingerings unless it is the only way or it follows standard fingering approach conventions, but i have to feel it out myself and usually as i work up a piece those may change since you will likely find better ways to finger it as you get the speed up or learn the music better and figure out even better ways to do it.