Tigranakert saw the rescue of part of the royal family, treasure, and harem by an elite cataphract cohort. The battle, if any, would have been one to the west of the Euphrates (LLL's Roman cohorts en route but before reaching Tigranakert) due to the contradiction between LLL's claim of having sacked T-kert and the still-standing famed temple of that city. True sacking came in the third quarter of the first cent. BCE with Antony.
Do not be surprised. Over one hundred thousand were able to live in complex cities of the first advanced Mesopotamian civilization (that of Sumer) in the third millennium BCE. That is one city in, granted, a very grain-producing rich area. Yet considering a conservative scaling to the area at least nominally ruled over by the Armenian "King of Kings" in the early to mid first cent. BCE would easily reach to and beyond the ten million marker. The Near East isn't as small as you may think it is (it is easy to think of the region as a relatively small one if your mental map is centered at the States, or Europe, or Russia, and so on).
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