In this work, we compare the first C-moments of the multiplicity distributions recently measured in proton-proton collisions at the LHC with the predictions of the Bialas-Praszalowicz model. In this model the multiplicity distribution is given by a negative binomial distribution (NBD). In our comparison, we try to identify the regions of the phase space where the NBD fails. We divide the data into three sets according to their phase space coverage: I: $p_T > 100 $ MeV and $|\eta|< 0.5$; II: $p_T > 100 $ MeV and $|\eta|< 2.4$ and II: $p_T > 500 $ MeV and $|\eta|< 2.4$. The mean multiplicity grows with the energy according to a power law and the power is different for each set.
The $C_n$ moments grow continuously with the energy, slowly in set I and faster in the other sets. We find that the NBD gives a very good description of the measured moments $C_2$, $C_3$ and $C_4$ and slightly overestimates $C_5$ in all data sets. The negative binomial parameter $k$ decreases continuously with the energy and there is no sign of change in this behavior.