I was watchin some clickbait veritasum youtube video about the 3n+1 problem. Basically, any number put through the algorithm will return to 1, but it's unproven and we only tested up to 2^60 or something. They talk about how one way to disprove the theory would be to find a counterexample, like a number where the algorithm goes to infinity instead of collapsing to 1.

What if when you get to high enough number, you find counterexample, and actually the frequency of counter examples increases. Like an unexpected property of extremely large numbers. Is it possible that for extremely large numbers there is like a "phase shift" that happens where they have completely unpredicted qualities that sets them apart from more common numbers? Like for example maybe the frequency of primes starts to increase or something of that nature? wouldn't that be trippy