All of us use the same keyboards more or less, maybe us randomly typing a large number is not as random as we would like to think. Just like how “asdf”, “xcyb” are common strings because these keys are together, there has to be some pattern here as well.
Especially for those very large numbers in the top ten (like 166884362531608099236779 with 6779 searches), and the relatively small number of total "votes" (probably less than a million), I think the only likely explanation for their rank is ballot-stuffing.
That means there is less entropy than purely random strings, not that this specific number would be so far outside the distribution. My money would be on someone hammering it.