For some applications that use pseudorandom numbers it is essential to keep the record of numbers generated so far. Such a representative example is cryptanalytic TMTO approach. In order to save the space, instead of straightforward recording of individual numbers generated, an ordered tree-like data structure which tracks the intervals of generated numbers is proposed. For estimating the memory requirements of this structure as a function of pseudorandom numbers range size, an analytical probabilistic model is established and used. This model determines the maximum number of intervals during recording which corresponds to the tree size. The result obtained from analytical model is fully validated experimentally by means of simulation for a wide spectrum of range sizes.