A strengthening the one of a theorem of Bourgain -Kontorovich
The following result is proved in this work. Consider a set of $\mathfrak D_N $ not surpassing the $N$ of the denominators of those ultimate chain fractions, all incomplete private which belong to the alphabet $1,2,3,5$. Then inequality is fulfilled $|\mathfrak{D}_N|\gg N^{0.99}$. The calculation, made on a similar Burgeyin theorem -- Of Kontorovich 2011, gives the answer $\mathfrak D_N \gg N^{0.80}$.