No, do a water change. Prime won't reduce anything. It makes ammonia non-toxic for 24 hours.
Thanks ValerieAdams ... HI Sanjay. It's nice to see you again. I'm not familiar with carbon dosing, and I couldn't be sure, but don't think Culprit has experience with it either. Both of us use chaeto to reduce nitrates, along with careful feeding, keeping mechanical filtration clean, and weekly water changes of about 20% of the tank's total volume.
You may want to do 2 larger water changes pretty close to each other to get your nitrate levels down. 50ppm is definitely too high, so I think I'd do a 40% change, wait 2 days, then do another 40% change.
Beyond bringing the level down, you'll need to work on keeping it from getting that high in the first place. Regular weekly water changes along with a careful feeding routine should help, as will the chaeto. Are you providing light for the chaeto?
Well, there are many ways of doing things, and carbon dosing, along with other ways of reducing nutrients in a tank, are all ways that aquarists might remove waste from the water so they don't have to do as many water changes. In my mind, this might be a good idea if I had a big tank that would be a lot harder and more expensive to do water changes on. Though, like any action we take with our tanks, there is the potential for good and bad or no result at all. If carbon dosing is the path you wish to take, I would highly suggest you put in a lot of research on the best method to achieve your goal. I am sorry that I cannot help you with it. I just haven't learned much about it as it is not something I want or need to do at this time.
However, I don't believe carbon dosing is the answer to 50ppm nitrates, and think a couple of water changes is the best answer for right now. Once your nitrates are down to a comfortable level, you will feel more comfortable and have time to read about carbon dosing.
Water changes in nano tanks are always the best way to go about it. Its easy, and quite literally nothing benefits a reef tank as much as regular water changes.
I'd follow what Stella said, and hopefully soon your chaeto will take off.