The Busy Beaver is a N state Turing Machine which starts with an all zero tape, and BB(N) is defined as the largest FINITE number of *1's* printed on the tape AFTER it halts.
BB(1)=1 BB(2)=4 BB(3) =6 BB(4)=13 BB (5) = 2098 Sometimes Busy beaver numbers are defined slightly differently is the maximum number of *steps* an in-state Turing machine makes before it halts then the first five busy beaver numbers are: - *Σ(1) = 1* - *Σ(2) = 6* - *Σ(3) = 21* - *Σ(4) = 107* - *Σ(5) = 47,176,870* *We know that at some point the Busy Beaver function starts growing faster than any computable function; nobody knows exactly when that happens but it's sometime before BB(643), probably much before. **There have been some very recent developments, in regard to BB(6), we still don't know what that number is but** we do have a better idea of what its lower bound is then we had a month ago. Before I can say what that is I have to say something about notation. Everybody knows that 10^15 means 10*10*10 15 times, but in this new notation 15^10 means a tower of iterated exponentiations 10 to the 10 to the 10 ...15 times.* *e* *So the new lower limit of the sixth busy beaver number is: * *BB(6)> 9^2^2^2* *I don't know this is a fact but I wouldn't be surprised if this was the largest finite number ever to come up in a mathematical investigation and not just in a contest to think of big numbers. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* wl' -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAJPayv0SGhrgRDRm029-_4O-ipV0jNcWQoLP%3DMnTzQEmE-HfTA%40mail.gmail.com.
