The big-numbers tag has no wiki summary.
9
votes
1answer
69 views
Examples of Diophantine equations with a large finite number of solutions
I wonder, if there are examples of Diophantine equations (or systems of such equations) with integer coefficients fitting on a few lines that have been proven to have a finite, but really huge number ...
24
votes
1answer
368 views
How do I calculate the 2nd term of continued fraction for the power tower ${^5}e=e^{e^{e^{e^{e}}}}$
I need to find the 2nd term of continued fraction for the power tower ${^5}e=e^{e^{e^{e^{e}}}}$ ( i.e. $\lfloor\{e^{e^{e^{e^{e}}}}\}^{-1}\rfloor$), or even higher towers. The number is too big to ...
2
votes
0answers
47 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
104 views
How can I calculate or think about the large number 32768^1049088?
I decided to ask myself how many different images my laptop's screen could display. I came up with (number of colors)^(number of pixels) so assuming 32768 colors I'm trying to get my head around the ...
0
votes
2answers
58 views
What is the biggest known safe prime number?
I am looking for the biggest known safe prime number. Can someone provide some reference to what that number is and a proof that it is indeed a safe prime number?
0
votes
1answer
45 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???
4
votes
3answers
161 views
Comparing $\large 3^{3^{3^3}}$, googol, googolplex
How to show that $\large 3^{3^{3^3}}$ (Third Ackermann number) is larger than a googol ($\large 10^{100}$) but smaller than googoplex ($\large 10^{10^{100}}$).
Thanks much in advance!!!
2
votes
1answer
310 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
101 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
83 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 ...
2
votes
2answers
475 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
83 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 $1000!$
1
vote
1answer
123 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
689 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 ...
1
vote
2answers
377 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.
-6
votes
7answers
361 views
What is the biggest classified number [closed]
For example millions is a class. So what is the biggest number class identified ? The classified biggest number in the universe.
4
votes
2answers
203 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
469 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
94 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 ...
2
votes
2answers
156 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 ...
3
votes
3answers
805 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
433 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:
$\sum\limits^{k}_{i=m}(N-i)^{k-i}(\frac{1}{N})^k\frac{k!}{(k-i)!i!} \leq a$
...
5
votes
3answers
1k 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
837 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 ...
40
votes
7answers
2k 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 ...
6
votes
4answers
2k 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.
