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We present results for the mass of the b quark in the scheme obtained by calculating the binding energy of the B meson in the static limit. The self energy of a static quark, needed for this purpose, is now known to O(α3) in the quenched approximation. We find a preliminary value of at nf = 0. The error is dominated by the remaining uncertainty in . In addition, using at O(α2), we estimate that the quark mass is reduced by approximately 70 MeV when two flavours of dynamical quarks are introduced.