In Gribov's scenario in Coulomb gauge, confinement of color charge is due to a long-range instantaneous color-Coulomb potential V(R). This may be determined numerically from the instantaneous part of the gluon propagator D_44,inst = V(R)δ(t). Confinement of gluons is reflected in the vanishing at k = 0 of the equal-time three-dimensionally transverse would-be physical gluon propagator D^tr(k). We present exact analytic results on D₄₄ and D^tr (which have also been investigated numerically, A. Cucchieri, T. Mendes, and D. Zwanziger, this conference), in particular the vanishing of D^tr(k) at k = 0, and the determination of the running coupling constant from x₀g²(k) = k² D_44,inst, where x₀ = 12N/(11N − 2N_f).