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These measurements are complemented by thermodynamic measurements of the specific heat on CeBi$_2$ at different pressures up to 2.55 GPa. For CeBi$_2$, we find a moderate increase of the antiferromagnetic transition, $T_\\text N$, from 3.3 K to 4.4 K by pressures up to 2.55 GPa. Notably, resistance measurements for both CeBi$_2$ and LaBi$_2$ show signatures of superconductivity for pressures above $\\sim$ 1.7 GPa. 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