Questions tagged [big-numbers]

Question 1

I recently got curious about understanding the growth rate of $\text{TREE(n)}$ (and/or the weaker $\text{tree(n)}$ with unlabeled trees). What I understood so far is that the existence and finiteness ...

Question 2

In googology many fast grwing functions are defined by graphs, for example the tree function and SCG, I would like to ask about a modification in this functions. A subcubic graph is a finite simple ...

Question 3

Is there an efficient method to compute the square root of a large power of two with the form $\lfloor\sqrt{2^{2n+1}}\rfloor$? Because $\lfloor\sqrt{2^{2n+1}}\rfloor = \lfloor\sqrt 2 (2^n)\rfloor$, if ...

Question 4

I want to compute the blocking probability \begin{align*} \operatorname{B}\left(\rho,m\right) & = \dfrac{\rho^{m}/m!} {\sum_{i= 0}^{m}\rho^{i}/i!} \\[5mm] \mbox{...

Question 5

I have recently found out about the TREE function, and how TREE(3) is unimaginably large. I also learned about Graham's number, which is a lot smaller than TREE(3). Yet, is there some way to find out ...

Question 6

Is there a good way to simplify the monstrous number $10^{2380849\cdot 10^{10^{120.20}}-1}$ using Knuth's Up-Arrow notation? I have tried to research how this could be done, but the notation still ...

Question 7

If $F(n)$ is the $n$-th Fibonacci number, then given $F(n)$ and $F(n-1)$, the classic "fast doubling" way of obtaining $F(2n)$ and $F(2n+1)$ is $$ \begin{align} F(2n) &= F(n) \left(2F(n+...

Question 8

In OEIS , the smallest even positive integers $k$ such that $k^{2^n}+1$ is prime are given upto $n=20$. Is there a known prime number with $n\ge 21$ ? Such a number would be very large , so I guess ...

Question 9

There are a variety of ways to define large numbers (https://en.wikipedia.org/wiki/Large_numbers), such as Graham's number, TREE(3), Rayo's number, etc. Often times we know the relative size of these ...

Question 10

Is $\text{BRANCH}(n)$ finite for $n > 2$? Define $\text{BRANCH}(n)$ as the maximum length of a string that is composed of at most $n$ unique characters AND meets the following condition: Define a ...

Question 11

Let's assume there is some non-standard model of the reals containing a number $N$ that is larger than any real number. Suppose $\exists N\in {^*}\mathbb{R} ( \forall r\in\mathbb{R}: r<N).$ Now I ...

Question 12

Define $f(k)$ to be the maximal natural number $n$ such that there exist $n$ strings $s_1,\dots,s_n$ from the alphabet $\{1,2\}$ such that no letter is repeated more than $3$ times in a row, for all $...

Question 13

Or more importantly, does it have a name? The function f(k)=x I have found goes under these rules, There is a group of n strings containing k characters Each string is 1 character longer than the ...

Question 14

Is it possible to calculate the leading decimal digits of $3 \uparrow\uparrow 5\ = 3^{3^{3^{3^3}}} = 3^{3^{7,625,597,484,987}}$? Using currently known methods, this would require knowing the complete ...

Question 15

I study mathematics, and I have a question: I have this math function: f(x) = floor(x^99999 / 10^(floor(log10(x^99999+0.1)) + 1 - 5)) (floor() is rounding down) ...

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Questions tagged [big-numbers]

$\text{TREE}(n)$ and well-quasi-ordered sets

What happens if we add vertex coloring to the Subcubic Graph Number (SSCG)?

Compute the square root of a large power of two

Approximation of blocking probability

How many layers of graham's number are required to beat TREE(3)?

Simplifying $10^{2380849\cdot 10^{10^{120.20}}-1}$ using Knuth's Up-Arrow notation

Fibonacci doubling using two squarings?

Is there a known generalized Fermat prime with exponent at least $2^{21}$?

Unsolved problems in the relative size of large finite integers

Is $\text{BRANCH}(n)$ finite for $n > 2$?

How big do hyper-reals get?

Does this text based Tree Function stay finite?

Does this "tree like" function stay finite?

Is it possible to calculate the first digits of this number?

How to get rid of large numbers in a function?

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