Comment by cperciva
1 day ago
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.
1 day ago
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.
And still that requires X to not be particularly large. It could conceivably be in ballpark of BB(40).
You, sir, have a very different definition of "not particularly large" than I do!
To be fair, BB(40) is smaller than almost all positive integers.
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This feels like saying there are probably hundreds of stars in the universe