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The value of BB(v), where BB is the Busy Beaver function, and v is the volume of the observable universe in planck length cubes, ought to suffice.

I hope you didn’t want a number you could actually figure out....

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Can't we keep on applying the BB function i.e BB(BB(BB(...(BB(v)))) given that every application of BB still results in a finite number?

Yes, and you can generalize this to BBN(v, N), which means N applications of BB to v. If we replace N with v, it becomes a single parameter BBN(v). Then we can apply this thing to itself, and so on. So, with any finite storage space, we can represent an arbitrarily large number in this fashion. Thus, finite storage does not set an upper bound on the number that can be represented.

yes, but "can" is rather optimistic.

The largest number I saw written out is the number of symmetries in the monster group, spelled out on wikipedia (iirc).

I'm actually going to say that's not a real number until you actually build that busy beaver. For one thing, the Bekenstein Bound is doing to come into play.

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