High-pressure discharge lamp, high-pressure discharge lamp lighting system and lighting equipment

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Disclosed is a high-pressure discharge lamp includes a translucent ceramics sealed container (1) provided with an enclosed part (1a) with a discharge space (1c) formed therein, a pair of electrodes (2) disposed inside of both end parts of the translucent sealed container (1), an ionization medium having a structure containing a metal halide that primarily emits light, a starting gas and substantially no mercury, the metal halide that primarily emits light including 30% by mass or more of a halide of at least one lanthanoid type rare earth metal and the starting gas having a pressure P (atm) satisfying the equation, 1 ≤ P ≤ 20, the ionization medium being sealed in the translucent ceramics sealed container (1), wherein the ratio D/G satisfies the equation, 0.3 ≤ D/G ≤ 2.4 when the maximum inside diameter of the translucent ceramics sealed container (1) is D and the inter-electrode distance is G.