On quadratic irrationalities having continued fractions with small periods

We study the class number of an indefinite binary quadratic form of discriminant $d$ based on the expansion of $\sqrt d$ into a continued fraction and single out sequences of $d$ for which $h(d)$ has a lower-bound extimate. Progress is made for the conjecture on the estimate of the quantity of prime discriminants $d$ with fixed length of period of expansion of $\sqrt d$.