# 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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### prime number (a form like Mersenne primes)

I found a form like Mersenne prime number and i wanted to be sure if its maybe better but i was wrong but still as good as Mersenne form its $(2^p+1)/3=P$ and p,P are primes P also can be a ...
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### Comparing power towers of $2$s and $3s$

Let $x=[x_1,x_2,...,x_n]$ be a finite list of positive real numbers, and define $\tau x$ as the power tower formed by these numbers. The function $\tau$ can be recursively defined by the following two ...
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### What is the chance that a number $P$ is prime if it's not divisible by any number less than $x$?

I am trying to check if a very big number ($>10^{10,000,000}$) is possibly prime. I have written a computer program to check if the number has any smallish (less than like $600,000,000$) factors......
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### calculating Modulus on Massive numbers [duplicate]

In the case I have two numbers large enough to justify using scientific notation twice $A \times 10^{B \times 10^C}$ or $Ae+Be+C$ How would I calculate Modulo without taking the numbers or any part of ...
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### Given that $2017$ is prime, how do I prove this statement?

I'm asked to prove the following statement: Let $N=(1008!)^2+1$. Prove that $N$ is divisible by $2017$. (Hint: $2017$ is prime.) I don't know how to go about proving this statement, since there seems ...
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### How to get the last $n$ digits of Ackermann function?

The Ackerman function is defined as follows: $$A(m,n)= \begin{cases} n+1,& m= 1\\ A(m-1,1), & m>0, n=0\\ A(m-1, A(m,n-1)), &m,n>0 \end{cases}$$ Is it possible to get the last ...
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### Is there a property relating gcd(a, b) % c and gcd(a %c, b%c) % c. Here all a,b,c are natural numbers i.e.>0 and '%' represents modulo operator.

I have been facing some difficulty solving problems relating the gcd and modulo operator. If I use the Euclidean algorithm then it works fine when either a or b is small because in one step itself a ...
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### How big are $f_3(3)$ and $f_4(4)$ in the fast growing hierarchy?

I read some articles about the fast growing hierarchy (and saw some vids), and I wonder how to calculate: $f_3(3)$ And especially $f_4(4)$ I know that there are huge numbers, but I wonder if someone ...
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### What is the largest number used in a useful mathematical proof that isn't just an upper or lower bound? [closed]

There are quite a few famous gigantic numbers used in useful mathematical proofs, like Skewes's number, Graham's number, and the number $2 \uparrow \uparrow 10^{10^6}$ from Coward and Lackenby's 2011 ...
1k views

### When does the busy beaver function surpass TREE(n)? [closed]

Since TREE is a computable function the BB function grows faster than it, but TREE seems to grow much more quickly early on, so when does Busy Beaver surpass it?
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### Sum of digits of sum of digits of sum of digits of $7^{7^{7^7}}$

On the back of a mathematical magazine, I came across some "quick facts" about the number 7. Most of them were real life related ones, like "Rome was buit on 7 hills", "the neck of most mamals is made ...