Editing Collatz conjecture (section)

===Experimental evidence===
The conjecture has been checked by computer for all starting values up to 2<sup>71</sup> ≈ {{val|2.36e21}}. All values tested so far converge to 1.<ref name=Barina>{{cite journal | last = Barina | first = David | title = Improved verification limit for the convergence of the Collatz conjecture | journal = The Journal of Supercomputing | year = 2025 | volume = 81 | issue = 810 | pages = 1–14 | doi = 10.1007/s11227-025-07337-0 | s2cid = 220294340 |url=https://link.springer.com/content/pdf/10.1007/s11227-025-07337-0.pdf }}</ref>

This computer evidence is still not rigorous proof that the conjecture is true for all starting values, as [[counterexamples]] may be found when considering very large (or possibly immense) positive integers, as in the case of the disproven [[Pólya conjecture]] and [[Mertens conjecture]].

However, such verifications may have other implications. Certain constraints on any non-trivial cycle, such as [[lower bound]]s on the length of the cycle, can be proven based on the value of the lowest term in the cycle. Therefore, computer searches to rule out cycles that have a small lowest term can strengthen these constraints.<ref name="Garner (1981)"/><ref name="Eliahou (1993)"/><ref name="Simons & de Weger (2005)"/>