One of the most common questions about Prezi is What is the best Prezi background image resolution?
Working with Prezi Next? Follow this updated tutorial on Prezi Next Best Background Image Size
To be honest, there really is no one size that fits all, but the Prezi manual often suggests to upload images smaller than 2880 by 2880 pixels and this includes backgrounds. However from my own experience I can say that usually nothing will happen if you upload something bigger. The transitions might get jagged, but if you are worried about that, then Prezi will also offer the chance to automatically Resize the image, once you upload a background. A general rule that I would recommend is to keep it less than 5000x5000px.
Background Image Size Tips
The most important thing about using Prezi backgrounds, whether they are 1000x1000px or 3000x300px images, is that you should always make sure all your content fits onto it. This can be done by selecting all content in the Prezi (Ctrl + a) and scaling it down. Now all the content will stay on the background and the edges of the background won’t be visible during some large scale transitions. To prevent that, you can also change the default Prezi background color. When you zoom/pan/move too far from the background image, then the background color will still be visible. So let’s say you have a background with very dark edges, you can change the background color also to black, and when accidentally the background image proves to be small during the transitions, then people won’t even notice it, because you are using a similar color.
View the example here: