When constraining the primordial non-Gaussianity parameter f_NL with cosmic microwave background anisotropy maps, the bias resulting from the covariance between primordial non-Gaussianity and secondary non-Gaussianities to the estimator of f_NL is generally assumed to be negligible. We show that this assumption may not hold when attempting to measure the primordial non-Gaussianity out to angular scales below a few tens arcminutes with an experiment like Planck, especially if the primordial non-Gaussianity parameter is around the minimum detectability level with f_NL between 5 and 10. In future, it will be necessary to jointly estimate the combined primordial and secondary contributions to the CMB bispectrum and establish f_NL by properly accounting for the confusion from secondary non-Gaussianities.

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