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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0
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1answer
154 views

Ackerman numbers, arrow notation

How to compare 3^3^3^3 and to 3↑(3↑↑3). (Ackerman number, arrow notation) Are these two numbers equal??? How to compare 3↑(3↑↑3) with googol and googolplex???
3
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3answers
234 views

Comparing $\large 3^{3^{3^3}}$, googol, googolplex

How to show that $\large 3^{3^{3^3}}$ is larger than a googol ($\large 10^{100}$) but smaller than googoplex ($\large 10^{10^{100}}$). Thanks much in advance!!!
2
votes
1answer
695 views

How to calculate modulo of large integer (number having 25000 digits)

I'm looking for solution to a problem to calculate modulo of very large number that can contain 25000 digits or less (n) with 10 digit number (m). ( n % m ) ? Pointer to appropriate theory resource ...
0
votes
1answer
149 views

Mix of Modulus and Division

While solving problems in SPOJ, I faced cases where I need to take Modulus of Big numbers like Fibonacci with 10^9 + 7 ( say MOD ). Now, consider the following case : (Fib(n) + Fib(6*n-1)) / ...
4
votes
1answer
116 views

Are there any secure ciphers you can use without a computer?

I have some kids that like encryption schemes such as the Caesar cipher and the Vigenère cipher. I would like to teach them something that's not easily breakable by todays maths and computers, but I ...
3
votes
2answers
2k views

How to handle big powers on big numbers e.g. $n^{915937897123891}$

I'm struggling with the way to calculate an expression like $n^{915937897123891}$ where $n$ could be really any number between 1 and the power itself. I'm trying to program (C#) this and therefor ...
0
votes
1answer
162 views

How to compare big numbers that are outcome of different functions.

How is the best way to compare big numbers? They are result of two functions with different asymptotic growth. For example: Googleplex which is $10^{{10}^{100}}$ to $1000!$
12
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1answer
900 views

Graham's Number : Why so big?

Can someone give me an idea of how R.Graham reached Graham's Number as an upper bound on the solution of the related problem ? Thanks !
1
vote
1answer
228 views

Normalize only big numbers for plotting

I have a set of numbers: [9, 8, 6, 4000] I want to plot a bar chart and I want to normalize only the 4000 number to 4, so the range of Y axis will be [0, 9]. Under the 4 bar I would write * 1000 so ...
3
votes
1answer
4k views

Large numbers in real world

I am a high school math teacher and I am looking for a comprehensive list of large numbers which occur in real world. For example There are $10^{14}$ cells in the human body $10^{100}$ is called ...
2
votes
3answers
2k views

Find modulo of multiplication of two number?

Given $m$, $a$ and $b$ are very big numbers, how do you calculate $ (a*b)\pmod m$ ? As they are very big number I can not calculate $(a*b)$ directly. So I need another method.
4
votes
2answers
228 views

RSA: Creating a key of desired length

Thanks and with respect to the users of this site, I've succeeded in creating an Encryption/Decryption procedure for the RSA algorithm. I also implemented a Miller-Rabin probabilistic primality test. ...
2
votes
1answer
2k views

Calculate the root of a number without useing the root function or decimal numbers

I'm trying to build a program in c# which will calculate prime numbers for me. I'm using the BigInteger class to work with 'endless' numbers. However, there is a big down side on this function, I ...
2
votes
1answer
105 views

Is the estimation of number's name's length and comma-grouping feasible?

I am thinking in a mathematical problem that probably is already formulated and even solved. It is about big integers and someting else. Let n be an integer positive number. For n := 1,000 we have ...
28
votes
3answers
1k views

Which is bigger: $9^{9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}}}$ or $9!!!!!!!!!$?

In my classes I sometimes have a contest concerning who can write the largest number in ten symbols. It almost never comes up, but I'm torn between two "best" answers: a stack of ten 9's (exponents) ...
2
votes
2answers
171 views

Making sense of combinatorics-based marketing hyperboles

Diablo 3 has 97 billion possible skill/trait builds. Per class. LessPop_MoreFizz, emphasis is mine. I used base two logarithm to claim "97 billion" configurations only are roughly 37 binary ...
5
votes
3answers
1k views

Estimating a certain row of Pascal's triangle

I need to calculate all the numbers in a certain row of Pascal's triangle. Obviously, this is easy to do with combinatorics. However, what do you do when you need to estimate all the numbers in, say, ...
3
votes
1answer
588 views

How to solve an inequality containing the sum of factorials and powers

In previous question, I asked how one would simplify the following equation for the case where the variables are very big: $\sum\limits^{k}_{i=m}(N-i)^{k-i}(\frac{1}{N})^k\frac{k!}{(k-i)!i!} \leq a$ ...
6
votes
4answers
6k views

How to simplify or calculate a formula with very big factorials

I'm facing a practical problem where I've calculated a formula that, with the help of some programming, can bring me to my final answer. However, the numbers involved are so big that it takes ages to ...
3
votes
2answers
1k views

How to explain Real Big Numbers?

Mathematicians, and esp. number theorists, are used to working with big numbers. I have noted on several occasions that lots of people don't have a clear understanding of big numbers as far as the ...
62
votes
5answers
5k views

Is it possible to represent every huge number in abbreviated form?

Consider the following expression. 16313107343153908912074032799466965289077771751767944648966669091376847859711382649033004075188224 This is a 98 decimal digit number. This can be represented as ...
8
votes
4answers
9k views

What is the biggest number ever used in a mathematical proof?

Probably a proof (if any exist) that calls upon Knuth's up-arrow notation or Busy Beaver.