We present results of 2 mm observations of the Crab Nebula, obtained using the Goddard-IRAM Superconducting 2 Millimeter Observer (GISMO) bolometer camera on the IRAM 30 m telescope. Additional 3.3 mm observations with the MUSTANG bolometer array on the Green Bank Telescope are also presented. The integrated 2 mm flux density of the Crab Nebula provides no evidence for the emergence of a second synchrotron component that has been proposed. It is consistent with the radio power law spectrum, extrapolated up to a break frequency of log(nu_{b} [GHz]) = 2.84 +/- 0.29 or nu_{b} = 695^{+651}_{-336} GHz. The Crab Nebula is well-resolved by the ~16.7 beam (FWHM) of GISMO. Comparison to radio data at comparable spatial resolution enables us to confirm significant spatial variation of the spectral index between 21 cm and 2 mm. The main effect is a spectral flattening in the inner region of the Crab Nebula, correlated with the toroidal structure at the center of the nebula that is prominent in the near-IR through X-ray regime.
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