  We derive a fast way for measuring primordial non-Gaussianity in a nearly
full-sky map of the cosmic microwave background. We find a cubic combination of
sky maps combining bispectrum configurations to capture a quadratic term in
primordial fluctuations. Our method takes only N^1.5 operations rather than
N^2.5 of the bispectrum analysis (1000 times faster for l=512), retaining the
same sensitivity. A key component is a map of underlying primordial
fluctuations, which can be more sensitive to the primordial non-Gaussianity
than a temperature map. We also derive a fast and accurate statistic for
measuring non-Gaussian signals from foreground point sources. The statistic is
10^6 times faster than the full bispectrum analysis, and can be used to
estimate contamination from the sources. Our algorithm has been successfully
applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu et al.
(2003).
