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For each n, there exist at least 4(n − 1)! n-state busy beavers. ... This number has 10⇈14 digits and is unreasonable to use in a computation. The value of S ...
However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers, the latter of which grow faster than any computable sequence ...
With protection in the late 19th and early 20th centuries, the current beaver population has rebounded to an estimated 10 to 15 million; this is a fraction of the originally estimated 100 to 200 million North American beavers before the days of the fur trade.
The connection is made through the Busy Beaver function, where BB(n) is the maximum number of steps taken by any n state Turing machine that halts. There is a 27-state Turing machine that halts if and only if Goldbach's conjecture is false.
An example of a "little" busy beaver -- a one, two, three, or four-state busy beaver -- can be "run" on any spreadsheet such as Excel. Five and six-state busy beavers cannot -- their "productions" -- the numbers of ones they can print -- are too huge to fit. You will need some help setting a model up.
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A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
47,176,870 = fifth busy beaver number [33] 47,326,700 = first number of the first consecutive centuries each consisting wholly of composite numbers [ 34 ] 47,326,800 = first number of the first century with the same prime pattern (in this case, no primes ) as the previous century [ 35 ]