For the case of closed Friedmann models with the cosmological constant, an 'N - λ' dependence is plotted, where N is the conformal time of existence of the Universe, and λ is the ratio of the cosmological constant to its Einstein's value. The observational properties of the asymptotic model of the first kind (the so-called Al model) corresponding to the maximum of this dependence are analyzed. For the matter-dominated models, the maximum is achieved at the point λ = 1. Formulae for the calculation of the age of the Universe and for that of the photometric distance in the Al model are deduced. The observational properties of the A1 model are compared to the corresponding properties of the standard cosmological model (λ = 0) which does not occupy any special distinguished position on the 'N - λ' diagram. It is shown that from the standpoint of the modern observational cosmology these two models cannot be told one from another. However, the A1 model has better standing from the viewpoint of the 'strong' wordings of the anthropic cosmological principle.