While Prime does fix the ammonia for a short amount of time, you shouldn't rely on it instead of water changes. The underlying cause of the ammonia is still there.
I see so many people recommending Prime because it detoxifies ammonia but I guess I don't understand why that is a good thing (unless you have ammonia in your tap water) instead of doing the water changes. Personally I dislike Prime because it leaves a nasty oily coating on top of the water that just grosses me out, it's to much like chemicals sitting on top of the water for me, even with the flow from the filter. So far it's the only water conditioner to leave that icky film.
If you do indeed have a fish in the tank while trying to cycle it, you can get some of the Safe Start bacteria to help jump start the cycle. Sometimes it helps and sometimes it doesn't in getting the cycle jump started.
Mainly just check the water everyday or every two days for the ammonia. When you stop seeing ammonia and start seeing nitrates, you have an established cycle and can go back to doing your once or twice weekly water changes.