Famous conjecture

This section groups conjectures that are famous, solved or unsolved.

They are usually conjectures that have a strong intuitive reasoning, but took a very long time to prove, despite great efforts.

The list: en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.

We ust use the if mod notation definition as mentioned at: math.stackexchange.com/questions/4305972/what-exactly-is-a-collatz-like-problem/4773230#4773230

Described at: arxiv.org/pdf/2107.12475.pdf where a relation to the Busy beaver scale is proven, and the intuitive relation to the Collatz conjecture described. Perhaps more directly: demonstrations.wolfram.com/CollatzSequenceComputedByATuringMachine/