  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.
