  The summary of the available semi-analytical results for the three-loop
corrections to the QCD static potential and for the $\mathcal{O}(\alpha_s^4)$
contributions to the ratio of the running and pole heavy quark masses are
presented. The procedure of the determination of the dependence of the
four-loop contribution to the pole-running heavy quarks mass ratio on the
number of quarks flavours, based on application of the least squares method is
described. The necessity of clarifying the reason of discrepancy between the
numerical uncertainties of the $\alpha_s^4$ coefficients in the mass ratio,
obtained by this mathematical method by the direct numerical calculations is
emphasised.
