# Questions tagged [big-numbers]

For questions relating to the computation, estimation and properties of extremely large finite quantities that are not usually used in mainstream mathematics. This is not for questions that just have large numbers; the fact that a number is very large has to affect the question.

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### Implementing binary splitting

I found out this article which says that binary splitting can be used to compute operations on numbers with high precision (sort of BigNum), such as exponential, trigonometric functions and constants (...
• 1
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### Calculate two to the power of decimal

I have a decimal number $a$ with integer and fractional parts as follows: $$a_{int} = a_0 + a_1 2 + a_2 2^2 + \cdots$$ $$a_{fr} = \frac{a_{-1}}{2} + \frac{a_{-2}}{2^2} + \cdots$$ I want to ...
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1 vote
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### How to understand the fast divisibility check for a double-width dividend?

I found this algorithm from the GNU factor utility. Given a double width dividend $n=n_1B + n_0$ and a single width odd divisor $d$, where $n_1, n_0, d < B=2^w, 2\nmid d$. Then with the precomputed ...
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1 vote
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### Rightmost decimal digits of Graham's number

How to find rightmost $n$ decimal digits of Graham's number efficiently. The last 500 digits are on the wiki/Graham's_number, but I want to know more. PowerTowerMod seems to be able to do it but is ...
• 845
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### Can someone explain TREE(3) in extremely simple terms?

I have recently begun getting interested in the field of googology, or as your tags list it, "big numbers." One of the first things I saw mentioned was the famous TREE(3) function. I am at a high ...
• 131
Let $TREE(n)$ and $tree(n)$ are Kruskal' tree sequences. The second one is called weak. Prove that $TREE(3)>tree^{tree^{tree^{tree^{tree^{8}(7)}(7)}(7)}(7)}(7)$ You can see that inequality in ...