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We study the effects of pressure on the electron-phonon interaction in MgB_2 using density-functional-based methods. Our results show that the superconductivity in MgB_2 vanishes by 100 GPa, and then reappears at higher pressures. In particular, we find a superconducting transition temperature T_c ~ 2 K for mu*=0.1 at a pressure of 137 GPa.

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