Biggest number in computer ever

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!

Bits are not numbers. You, as a programmer, give them the meaning you want, possibly numbers.

Now, I decide that 1 represents "the biggest number ever thought by a human plus one".

Errr this is a five year old?

How about something along the lines of: "I'd love to tell you but the number is so big and would take so long to say, I'd die before I finished telling you".