The great thing about using a technology myself, for a real purpose rather than testing, is that I learn things I wouldn't otherwise. Last week I made my first real Prezi and today I learned that to share a Private Prezi, you need to use the URL found by clicking the Share button (below) rather than the URL in the address bar. If you use the URL in the address bar, people will get the "Prezi Not Found" page.
Then you'll get this screen below which has the URLs to share the Prezi for others to view it or to edit it. It is a longer URL than the one at the top of the screen. You can also email it through here. Then there is a link to add editors in the other tab.
It's nice to have a "reset share links" option, so that you can give it a new link for whatever reason. Maybe someone posted it somewhere you did not want it to go - with this option you can disable the old link without having to take the Prezi down.
Below is what you see when you click the options at the top right. The bottom option, Private, is the one that you need the specific URL for.
Maybe this was obvious to others all along and something I just realized or maybe it was a recent change. Prezi has changed a few times since I've started training on it and I never received any notification about the changes. Each change has been for the better but it's a little disconcerting to discover the program is different when training on it in front of a group. Keeps me on my toes!