  We show a primordial non-linear "f_NL" term may produce unphysically large
CMB anisotropy for a red-tilted primordial power spectrum (n<1), because of
coupling to primordial fluctuation on the largest scale. We consider a
primordial power spectrum models of a running spectral index, and a transition
at very low wavenumbers. We find that only negative running spectral index
models are allowed, provided that there is no transition at a low wavenumbers
(i.e. k<<1). For models of a constant spectral index, we find log(k_c/k_0)>
-184, at 1 sigma level, on the transition scale of sharp cut-off models, using
recent CMB and SDSS data.
