[cperciva]

A counterexample of the form "X cycles to X after N steps" is easy to check. A counterexample of the form "starting with X we keep going up forever" is hard to check in finite time.

[IsTom]

And still that requires X to not be particularly large. It could conceivably be in ballpark of BB(40).

[AnimalMuppet]

You, sir, have a very different definition of "not particularly large" than I do!

[Sharlin]

To be fair, BB(40) is smaller than almost all positive integers.

[db48x]

It’s practically zero, in fact.

[jonathrg]

This feels like saying there are probably hundreds of stars in the universe