This dataset provides two complementary all-sky catalogs of primary red clump (RC) stars derived from Gaia DR3 low-resolution BP/RP (XP) spectra. A mixture density network (MDN), trained using the erratum-corrected asteroseismic cross-matched catalog of Ting et al. (2018), infers spectroscopic estimates of ΔΠ1, the asymptotic period spacing of dipole gravity modes, and Δν, the large frequency separation, from each 343-dimensional corrected XP spectrum. Primary RC stars are selected using ΔΠ1_pred ≥ 250 s and Δν_pred < 5.5 μHz, together with thresholds on the width of the selected ΔΠ1 Gaussian component. The high-purity Tier 1 catalog contains 532,189 stars with 97% purity, while the high-completeness Tier 2 catalog contains 6,534,931 stars with 86% completeness and 84% purity. Both catalogs include Gaia DR3 astrometry, atmospheric parameters from Zhang and Green (2025), MDN-inferred seismic parameters, selected-component widths, the mixing weight of the selected ΔΠ1 component, Ks-band extinction, calibrated absolute magnitude, and photometric distance with its uncertainty. The median photometric distance precision is approximately 6% for Tier 1. The catalogs provide homogeneous, full-sky tracer samples for studies of Galactic structure, chemical evolution, stellar populations, and dynamics.