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We observed visible second-harmonic and ultraviolet third-harmonic fields generated in reflection from the surface of a two-dimensional triangular GaN/sapphire photonic crystal. When the pump radiation resonates with a photonic mode, enhancement factors as high as 250 and 3500 occurred for the second- and third-harmonic signals, respectively, as compared to the unpatterned GaN slab. The very large increase of third-harmonic field, with a photon energy exceeding that of the electronic band gap, was used as an efficient mechanism to induce GaN photoluminescence.