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We compute the large-$N$ limit of the QCD chiral condensate on the latticeusing twisted reduced models, and performing controlled continuum and chiralextrapolations. We perform two different calculations: one consists inextracting the chiral condensate from the quark mass dependence of the pionmass, and the other consists in extracting the chiral condensate from thebehaviour of the mode number of the Wilson-Dirac operator for smalleigenvalues. We find consistency between the results of the two methods, givinga joint estimate of $\lim_{N\to\infty}\Sigma(N)/N=[184(13)$ MeV$]^3$($\overline{\mathrm{MS}}$, $\mu=2$ GeV, taking the square root of the stringtension $\sqrt{\sigma}=440$ MeV to set the scale), in remarkable agreement withthe $\mathrm{SU}(3)$ 2-flavor FLAG result.

The large-$N$ limit of the chiral condensate from twisted reduced models