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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What is the smallest prime factor of the number $14^{14^{14}}+13\ $?

What is the smallest prime factor of the number $$N\ :=\ 14^{14^{14}}+13\ ?$$ The number of digits of $N$ is $12,735,782,555,419,983$ (The number of digits of $N$ has itself $17$ digits). The first ...
4
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164 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 ...
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67 views

Does Graham's number have an odd or an even number of digits?

I think it is hopeless to decide whether the number of digits of Graham's number is even or odd because the only way that I can think of is determining the logarithm with accuracy $0.1$ or even ...
3
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570 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
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54 views

Can I restrict the possible factors of $2\uparrow \uparrow 4+3\uparrow \uparrow 4$?

I would like to accelerate the search of prime factors of $$2\uparrow \uparrow 4+3\uparrow \uparrow 4$$ In a question, I asked for a prime factor and another user also asked, whether this number is ...
2
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71 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 ...
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124 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 ...
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75 views

What is the smallest number $n$ , such that $n\uparrow^4 n>3\uparrow^5 3$ holds?

What is the smallest number $n$, such that $$n\uparrow^4 n>3\uparrow^5 3$$ holds ? $\uparrow$ stands for Knut's up-arrow-notation and is defined as follows $a\uparrow b=a^b$ $$a\uparrow ...
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55 views

For which natural numbers $m,n>1$ does the inequality $2\uparrow^m n>f_m(n)$ hold?

Denote $$f(n,m):=2\uparrow^{m-1} n$$ (See : Wiki ) and $$g(n,m):=f_m(n)$$ (See : Wiki ) It is straightforward to show $f(n,m)<g(n,m)$ for all $m,n>1$ via induction. But for which $m,n>1$ ...
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28 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 ...
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71 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 ...
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59 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 ...