We present kinetic Monte Carlo simulation data for the stationary rate J of two-dimensional nucleation of monolayer-thick crystal clusters in the growth of an atomically smooth (100) face of single-component Kossel crystal. The data are over a wide range of supersaturations s and effective broken-bond energies omega of nearest-neighbor atoms, and the J values span about 15 orders of magnitude. The simulation reveals that, in the s,omega range studied, the In J vs s curve is smooth but with nearly linear portions connected with rather sharply curved segments when the omega value is sufficiently great. The simulation J(s) data are used for verification of the classical (CNT) and atomistic (ANT) nucleation theories without free parameters. It turns out that whereas J is overestimated by CNT, it is underestimated by ANT. The disagreement between theory and simulation is much greater for CNT than for ANT and, with increasing omega, it increases for the former but almost disappears for the latter. However, the ANT prediction about broken linear In J vs s dependence is not confirmed by the simulation in the s,omega range-studied.