limit - Biggest number in computer ever

Question

Just asked by my 5 year old kid: what is the biggest number in the computer?

We are not talking about max number for a specific data types, but the biggest number that a computer can represent.

Infinity is not allowed.

UPDATE my kid always wants to print as well, so lets say the computer needs to print this number and the kid to know that its a big number. Of course, in practice we won't print because theres not enough trees.

question from:https://stackoverflow.com/questions/3708461/biggest-number-in-computer-ever

Answer 1

This question is actually a very interesting one which mathematicians have devoted a fair bit of thought to. You can read about it in this article, which is a fascinating and accessible read.

Briefly, a guy named Tibor Rado set out to find some really big, but still well-defined, numbers by defining a sequence called the Busy Beaver numbers. He defined BB(n) to be the largest number of steps any Turing Machine could take before halting, given an input of n symbols. Note that this sequence is by its very nature not computable, so the numbers themselves, while well-defined, are very difficult to pin down. Here are the first few:

BB(1) = 1
BB(2) = 6
BB(3) = 21
BB(4) = 107

... wait for it ...

BB(5) >= 8,690,333,381,690,951

No one is sure how big exactly BB(5) is, but it is finite. And no one has any idea how big BB(6) and above are. But at least these numbers are completely well-defined mathematically, unlike "the largest number any human has ever thought of, plus one." ;)

So how about this:

The biggest number a computer can represent is the most instructions a program small enough to fit in its available memory can perform before halting.

Squared.

No, wait, cubed. No, raised to the power of itself!

Dammit!