https://scottaaronson.blog/?p=8088 2024-07-02, BB(5) == 47,176,870. Nice explanation of why this is difficult: > The real difficulty is, how do you prove that some given machine runs forever? If a Turing machine halts, you can prove that by simply running it on your laptop until halting (at least if it halts after a โmereโ ~47 million steps, which is childโs-play). If, on the other hand, the machine runs forever, via some never-repeating infinite pattern rather than a simple infinite loop, then how do you prove that?
Busy Beaver (BB) the longest running turing machine with N states that does halt.
https://data.jigsaw.nl/Rado_1962_OnNonComputableFunctions_Remastered.pdf