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In this letter, we show theoretically how the light-confining properties of triply-resonant photonic resonators can be tailored to enable dramatic enhancements of the conversion efficiency of terahertz (THz) generation via nonlinear frequency down-conversion processes. Using detailed numerical calculations, we predict that this approach can be used to reduce up to three orders of magnitude the pump powers required to reach quantum-limited conversion efficiency of THz generation in conventional nonlinear optical material systems. Furthermore, we propose a realistic design readily accessible experimentally, both for fabrication and demonstration of optimal THz conversion efficiency at sub-W power levels.