We report measurements on ultrathin (<10 nm) nanowires produced by coating carbon nanotubes with a superconducting amorphous MoGe alloy. We find that nanowires can be superconducting or insulating depending on their normal state resistance compared to – the quantum resistance for Cooper pairs. If the tunneling of quantum phase slips (QPS) is prohibited due to strong damping, and so the wires stay superconducting. The insulating state, observed if , is explained in terms of proliferation of quantum phase slips and corresponding localization of Cooper pairs. The observed superconductor-insulator transition is analogous to the dissipative phase transition which takes place in Josephson Junctions at (Penttila et al., Phys. Rev. Lett. Vol.82, p.1004, 1999)

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