I feel the article is mixing up S(n) (max number of steps) and Σ(n) (max number of 1s written), going by the wikipedia article of BB https://en.wikipedia.org/wi

I feel the article is mixing up S(n) (max number of steps) and Σ(n) (max number of 1s written), going by the wikipedia article of BB https://en.wikipedia.org/wiki/Busy_beaver https://en.wikipedia.org/wiki/Busy_beaver Notably the list of BB numbers in the article matches the values of S(n) in wikipedia instead of Σ(n). Also this sentence makes more sense if you replace Σ(n) with S(n) > If after these steps the program hasn’t halted it means it’ll never halt (by the definition of the Σ(n)).