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The nuclear modification factor, RAA, of the prompt charmed mesons D0, D+ and D∗+, and their antiparticles, was measured with the ALICE detector in Pb-Pb collisions at a centre-of-mass energy sNN−−−√=2.76 TeV in two transverse momentum intervals, 5<pT<8 GeV/c and 8<pT<16 GeV/c, and in six collision centrality classes. The RAA shows a maximum suppression of a factor of 5-6 in the 10% most central collisions. The suppression and its centrality dependence are compatible within uncertainties with those of charged pions. A comparison with the RAA of non-prompt J/ψ from B meson decays, measured by the CMS Collaboration, hints at a larger suppression of D mesons in the most central collisions.