  Zaremba's conjecture (1971) states that every positive integer number can be
represented as a denominator (continuant) of a finit continued fraction with
all partial quotients being bounded by an absolute constant A. Recently (in
2011) several new theorems concerning this conjecture were proved by Bourgain
and Kontorovich. The easiest of them states that the set of numbers satisfying
Zaremba's conjecture with A = 50 has positive proportion in N. In 2014 the
author with D. A. Frolenkov proved this result with A =5. In this paper the
same theorem is proved with alphabet {1, 2, 3, 4, 10}
