When I read about collatz I wrote a C# program that short circuits the calculation like that, but my programming chops are not great and it could only handle 3000 digits of memory serves. It's somewhere on my GitHub page and I'm curious how many other people released similar code to speed things up.
I ended up using it to compare single core performance on any windows machine, because the timestamped logging was deterministic. Rewrote it in python and still use it these days.
Write a program that, for a positive integer, runs the Collatz process on it (if even: halve it; if odd, multiply by three and add one; repeat).
If the process results in a 1, move on to the next number and repeat.
If the process produces a number it produced previously, halt. (Worried you’ll need unbounded state for this part? Use tortoise+hare, it’s fine).
This program halts if and only if the Collatz conjecture is false.
Now, the Collatz conjecture might not be unprovable. But for now no human can tell you whether or not that program halts.