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In this Paper we consider a problem of formation and evolution of orbitalparameters of a binary primordial black hole (PBH) due to gravitationalinteraction with clustering cold dark matter (CDM). Mass and initial separationhave values, which are appropriate for the problem of explanation of theLIGO/Virgo events by coalescing binary PBHs. We consider both radiationdominated and CDM dominated stages of the evolution using numerical andsemi-analytical means. We show that at the end time of our numericalsimulations binary's semimajor axis decreases by approximately one hundredtimes, while its angular momentum decreases by ten times, in comparison to thestandard values, which do not take into account effects associated with CDMclustering. We check that our conclusions are hardly affected by numericalartefacts. We estimate the merger rate of binary PBHs due to emission ofgravitational wave at the present time both in the standard case when theeffects associated with clustering are neglected and in the case when they aretaken into account and show, that these effects could increase the merger rateat least by $6-8$ times in comparison to the standard estimate. This, in turn,means, that a mass fraction of PBHs, $f$, should be smaller than it was assumedbefore.

The evolution of a primordial binary black hole due to interaction with cold dark matter and the formation rate of gravitational wave events