  We discuss the problem for detecting long-range correlations in sequences of
values obtained by generators of pseudo-random numbers. The basic idea is that
the H{\"o}lder exponent for a sufficiently long sequence of uncorrelated random
numbers has the fixed value $h=1/2$. The presence of long-range correlations
leads to deviation from this value. We calculate the H{\"o}lder exponent by the
method of multifractal detrended fluctuation analysis (MFDFA). We discuss
frequently used tests for randomness, finite sample properties of the MFDFA,
and the conditions for a correct application of the method. We observe that the
fluctuation function $F_{q}$ used in the MFDFA reacts to trends caused by low
periodicity presented in the pseudo-random number generator. In order to select
appropriate generators from the numerous programs we propose a test for the
ensemble properties of the generated pseudo-random sequences with respect to
their robustness against presence of long-range correlations, and a selection
rule which orders the generators that pass the test. Selecting generators that
successfully pass the ensemble test and have good performance with respect to
the selection rule is not enough. For the selected generator we have to choose
appropriate pseudo-random sequences for the length of the sequence required by
the solved problem. This choice is based on the closeness of the H{\"o}lder
exponent of the generated sequence to its value 1/2 characteristic for the case
of absence of correlations.
