N 3 f g 6 term in the pressure of hot QCD

We determine the first independent part of the g coefficient in the weak coupling expansion of the QCD pressure at high temperatures, the one proportional to the maximal power of the number of quark flavors Nf . In addition to introducing and developing computational methods that can be used in evaluating other parts of the expansion, our calculation provides a result that becomes dominant in the limit of large Nf and a fixed effective coupling g 2 eff gNf=2.