The pressure dependences of resistivity and ac susceptibility have been measured in the mineral calaverite AuTe$_2$. Resistivity clearly shows a first-order phase transition into a high-pressure phase, consistent with the results of a previous structural analysis. We found zero resistivity and a diamagnetic shielding signal at low temperatures in the high-pressure phase, which clearly indicates the appearance of superconductivity. Our experimental results suggest that bulk superconductivity appears only in the high-pressure phase. For AuTe$_2$, the highest superconducting transition temperature under pressure is $T_{rm c}$ = 2.3 K at 2.34 GPa; it was $T_{rm c}$ = 4.0 K for Pt-doped (Au$_{0.65}$Pt$_{0.35}$)Te$_2$. The difference in $T_{rm c}$ between the two systems is discussed on the basis of the results obtained using the band calculations and McMillans formula.
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