For questions relating to the computation, estimation and properties of extremely large quantities that are not usually used in mainstream mathematics.

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3
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1answer
21 views

Predicting how long the result of a permutation

We're calculating the result of a 'tweaked' Birthday Problem, but when we're calculating, we stumped by a very nasty permutation. $$10^{576}P_{10^{16}}$$ Which, make us stop working at the number, ...
2
votes
1answer
78 views

Graham's Number versus another large number

I recently read this article about the most damage you can do in a single turn in Magic the Gathering. According to the current version of the deck, that damage is about a) $2 \rightarrow 17 ...
1
vote
1answer
91 views

Divisibility of huge numbers

Please help me to solve my homework ;) Prove that for any positive integer $n$ a square of rather big number divides even more huge number: $${\LARGE \left.\underbrace{33\dots 3}_{1\underbrace{00\dots ...
4
votes
0answers
133 views

Transfinite Knuth-arrow hierarchy vs. fast-growing hierarchy

Suppose Knuth arrow notation (and hence the hyperoperation sequence) is extended to transfinite ordinal indices as follows: Let μ be a large countable ordinal such that a fundamental sequence is ...
3
votes
0answers
437 views

First $n$ digits of Graham's Number

I know using Euler's Totient function, it's easy to find the last $n$ digits of Graham's number (or any large repeating power tower), but is there any known way to find the first $n$ digits of ...
2
votes
0answers
69 views

Improving Montgomery product

I am reading the paper "A Cryptographic Library for the Motorola DSP56000" (http://link.springer.com/content/pdf/10.1007%2F3-540-46877-3_21.pdf) which describes a trick to speed-up calculation of the ...
1
vote
0answers
98 views

Tim Chow's proof that the moser-number is much smaller than grahams number

The link here shows a proof from Tim Chow that the moser-number is much smaller than grahams number. I do not understand the inequality 3^^...^^3 (3^^^^^3×2-1 arrows) << G 2 What does G 2 ...
0
votes
0answers
7 views

Comparing conway chains

See https://en.wikipedia.org/wiki/Conway_chained_arrow_notation for the details how conway chained arrow notation works. I want to calculate the approximate value $n$ such that $$n\rightarrow ...
0
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0answers
41 views

Node potentials of minimum cost flow successive shortest path algorithm

I have a simple directed graph $G(V,E)$ that has a source $s$ and sink $t$. Each edge $e$ of $G$ has positive integer capacity $c(e)$ and positive integer cost $a(e)$. I am trying to find the minimum ...
0
votes
0answers
12 views

Check for greatest common multiple in a range

I am supposed to be writing a program that takes two numbers and checks to see if they have a common multiple in the range of 1 - 1100000000, 1.1 billion. If there are many common multiples, I have to ...
0
votes
0answers
64 views

What is the highest number that could be written down in principle using all computers in the world?

I read somewhere in the internet, that the capacity of all computers in the world would be about $10^{18}$ bytes. Does this mean, that in principle, a number with $10^{18}$ digits could be written ...
0
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0answers
51 views

monotony for conway chains

Let X and Y be chains, m and n be natural numbers with 0 < m < n. Is it always true that $$X \rightarrow m \rightarrow Y < X \rightarrow n \rightarrow Y$$ ? I need this to bound the ...