  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 McMillan's formula.
