On the german Wikipedia, I read that:

Der Bulgare Georgi Georgiev veröffentlichte 2003 eine Untersuchung, in der er fleißige Biber daraufhin analysierte, ob sie anhalten würden oder nicht.[2] Für {\displaystyle n=5}n = 5 entzogen sich lediglich knapp über 40 fleißige Biber einem gesicherten Ergebnis, da sie aufgrund besonderer Verhaltensweisen nicht mit den von Georgiev angewandten Methoden abschließend zu analysieren waren.

The same sentence doesn't appear in english, as far as I saw. The summary is that in 2003 BB(5) was almost determined, but there were still about 40 Turing machines (out of around 60 trillion) that evaded the proof regarding whether they halt.

Is this still the case or was the number at least reduced? What made those machines so difficult to analyze?


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