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I got the idea his BB_2 is different. He's referring to a super Turing machine that can solve the halting problem for non-super Turing machines.

The BB-2 used in an iterative algorithm is talking about "A busy beaver number of (A busy beaver number of 10)", no need for super machines here. The iterative algorithm is short enough you can define it in your 1000 characters, no need for additional publication.

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But the super Turing machines busy beaver numbers vastly outgrow your iterated busy beaver very quickly. It doesn't take that many states to write a program that can do an iterated function application, and to a super Turing machine, it's easy to write the busy beaver function.

OK, but as the article states you'll have to write a paper to a low-level journal to use it, and I'd have to be really into and good at mathematics to consider doing exactly that to win a name-the-biggest-number competition...

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