Alter: template type. Add: s2cid, doi, year, journal. Removed URL that duplicated unique identifier. Removed accessdate with no specified URL. | You can use this bot yourself. Report bugs here. | Suggested by SemperIocundus | via #UCB_webform
{{asof|2020}}, the conjecture has been checked by computer for all starting values up to 2<sup>68</sup>.<ref name=Barina>{{cite webjournal | last = Barina | first = David | title = Convergence verification of the Collatz problem | journal = The Journal of Supercomputing | year = 2020 | doi = 10.1007/s11227-020-03368-x | s2cid = 220294340 }}</ref> All initial values tested so far eventually end in the repeating cycle {{math|(4;2;1)}}, which has only three terms. From this lower bound on the starting value, a lower bound can also be obtained for the number of terms a repeating cycle other than {{math|(4;2;1)}} must have.<ref name=Garner>{{cite web |last=Garner |first=Lynn E. |title=On The Collatz 3n + 1 Algorithm |url=http://www.ams.org/journals/proc/1981-082-01/S0002-9939-1981-0603593-2/S0002-9939-1981-0603593-2.pdf |accessdate=27 March 2015}}</ref> When this relationship was established in 1981, the formula gave a lower bound of {{val|35400}} terms.<ref name=Garner/>
https://link.springer.com/epdf/10.1007/s11227-020-03368-x?sharing_token=iHjm8Jplv9xSWZdSO8qrDfe4RwlQNchNByi7wbcMAY6LaNX-8xpPpeFvzaIIiop25QUeUqGPXOS4Kq08iPtbRqCaH8c-hMRTHkRt8ubtqjX9EXGPlfre6lVPg9MZOQm9Z195-DciZygFzRX1hmq-HYF19Mpwv840K681gJnY3os%3D |accessdate=2 July 2020}}</ref> All initial values tested so far eventually end in the repeating cycle {{math|(4;2;1)}}, which has only three terms. From this lower bound on the starting value, a lower bound can also be obtained for the number of terms a repeating cycle other than {{math|(4;2;1)}} must have.<ref name=Garner>{{cite web |last=Garner |first=Lynn E. |title=On The Collatz 3n + 1 Algorithm |url=http://www.ams.org/journals/proc/1981-082-01/S0002-9939-1981-0603593-2/S0002-9939-1981-0603593-2.pdf |accessdate=27 March 2015}}</ref> When this relationship was established in 1981, the formula gave a lower bound of {{val|35400}} terms.<ref name=Garner/>
This computer evidence is not a proof that the conjecture is true. As shown in the cases of the [[Pólya conjecture]], the [[Mertens conjecture]], and [[Skewes' number]], sometimes a conjecture's only [[counterexamples]] are found when using very large numbers.
