  We compute the pressure and entropy of hot QCD in the limit of large number
of fermions, N_f >> N_c ~ 1, to next to leading order in N_f. At this order the
calculation can be done exactly, up to ambiguities due to the presence of a
Landau pole in the theory; the ambiguities are O(T^8/\Lambda^4_{Landau}) and
remain negligible long after the perturbative series (in g^2 N_f) has broken
down. Our results can be used to test several proposed resummation schemes for
the pressure of full QCD.
