By using highly sensitive millikelvin superconducting quantum interference device magnetometry, the magnitude of the Curie temperature as a function of the Mn concentration x is determined for thoroughly characterized Ga 1−x Mn x N. The interpretation of the results in the frame of tight-binding theory and of Monte Carlo simulations allows us to assign the spin interaction to ferromagnetic superexchange and to point out the limited accuracy of state-of-the-art ab initio methods in predicting the magnetic characteristics of dilute magnetic insulators.