Earth Prime is the Earth that exists in Batman's dimension, and is the home of the DC Universe. While similar in many ways, Donatello notes that it has different countries, different cities, celebrities and even periodic elements to the Turtles' native world and dimension. One major difference is the prevalence of superheroes and super villains, which are mostly nonexistent in the Turtles' own world. Another is the existence of Gotham City, which does not exist at all on the Turtles' Earth.
Mutants are not able to live in Earth Prime for more than a few weeks. The mutagen in their bodies becomes inert after a period, causing them to revert back to their original forms.