# Questions tagged [big-numbers]

Questions about or involving outside the range of normal machine precision, using Mathematica's capacity for arbitrary precision numbers and numbers outside the normal range of floating-point arithmetic.

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### How to compare power towers in Mathematica?

First I tried it directly, but it overflowed: ...
96 views

### How to deal properly with big integer limitations [closed]

I need to run an algorithm that manipulates digits with big integers and integer functions, And I need to be careful to avoid erroneous results in my research. It is not necessary to answer every ...
163 views

### How to prevent spikes in memory usage during simple numerical evaluation?

I've noticed strange peaks in memory usage (several GB) during evaluation of my code, sometimes freezing operating system. Nailed it down to numerical evaluation of "bignum" expressions like this: <...
158 views

### How to stop calculating if there're some large number?

I want to calculate something like o[n, o[n, o[n, n]]] Where n means a number and o means a ...
89 views

### Algorithm that will trim a unique ID number and produce a shorter unique ID

I have a unique ID number with 2^128 magnitude length (128 bits). This means ~3.4e+38 which is quite large that my actually needs, spending valuable time in a transmission protocol. There is a ...
177 views

### How to loop through a large number in mathematica

I am trying to find all divisors of 200! [Project Euler, problem 608 - in case anybody is curious]. It has many divisors and hence using ...
55 views

### Code needed to determine the smallest k that the equation will fail by brute force [closed]

I find one of the suggested solution to this problem a little bit questionable: “If N is divisible by 1, 2, 3,. . . M, then N must also be divisible by M + 1, M + 2, M + 3, . . . M + k for k is a ...
589 views

### Is there a command that does exact numerical conversion of non-exact to exact numbers?

I generally prefer to do all my intermediate calculations with exact numbers, and then round my result at the end. Thus I will typically convert each arbitrary-precision number to its exact equivalent;...
296 views

### Integrate over sharp peak [closed]

Hi I have a function that has a sharp spike. I need to NIntegrate over the peak but it seems that NIntegrate does not handle it well. Actually as far as I can tell, even the evaluation of the ...
28 views

### How to solve equations in Gaussian integers modulo p efficiently [duplicate]

This question is related to my previous question which can be found here. Calling the function sols1 = gaussianPowerModList[I, 8192, 18446744069414584321];] ...
271 views

### How to solve equations in Gaussian integers modulo p

How to solve a complex equation of the form: $$z^n \equiv i \pmod p$$ where $z$ is a Gaussian integer, $i$ is the imaginary number, $n, p \in \mathbb{Z}^+$ and $p$ is prime. I am dealing with quite ...
14k views

### How to calculate extremely large exponential

I would like to calculate the following nested exponential: $$\Large{e^{e^{10^{72}}}}$$ In case that might be hard to read, in Mathematica functional notation it is: ...
170 views

### Plot for big x numbers

I want to make a plot of data with big values by x. My code is this ...
7k views

### How to express an integer number in English words?

How do I convert a number to a readable string? I would like to implement a function, inWords[], inWords[n_]:= ? which ...
110 views

### Exporting large numbers to .PDF file

For educational purpuses I sometimes print out large or interesting numbers for young mathematicians participating in classes. The numbers are generated in Mathematica. I have tried simply copying ...
269 views

### Efficiently checking whether a number is a perfect power

Goal The goal is to efficiently check whether a number is a perfect power. Attempts It is possible to check whether a number is a perfect power using ...
1k views

### Number of digits for factorial of 12345678987654321

What is the number of digits (IntegerLength) of the factorial of 12 345 678 987 654 321? The number of zeros at the end of this factorial was calculated and it is huge: exactly 3 086 419 746 913 569 ...
330 views

### How to generate random natural numbers in $[1, \infty)$? [closed]

Functions like RandomInteger draw random variates from a finite range. Can one also obtain random natural numbers in case the range extends from 1 to infinity? If ...
5k views

### What is so special about Prime?

When we try to evaluate Prime on big numbers (e.g. 10^13) we encounter the following issue: ...
97 views

### Is the arbitrary base that can be defined by IntegerLength[n,base] really limitless?

I am going to be working with very large numbers, and would like write the input in the base 10 and have the computer output in another arbitrary base. If it truly is limitless, that would be awesome ...
237 views

### Datatypes and numbers in Mathematica

I have some questions about numbers in Mathematica: Does Mathematica work with datatypes like int, long, ...
2k views

### The biggest exponent that can be computed

I am struggling with my crypt assignments and constantly getting overflow errors. Below is a simplified version of the problems I am experiencing ...
855 views

### Faster binary Hamming weight for big integers?

While working on an answer to Count the sequences in an array I found that DigitCount was the bottleneck in my code when used as ...
244 views

### How to further accelerate arithmetic with Fermat Pseudoprime and Fibonacci number

I've been working on this all night, and I have made this go pretty fast, compared to my first iteration of the program, but now I'm out of ideas. I'm trying to write a program to test (by good old ...
686 views

### How do I find my maximum precision on my computer? [duplicate]

I'm trying to run this ...
611 views

### Fast Trial Division

I'm going to write a custom Trial Division primality test. I know that PrimeQ will first try trial division and then switches to ...
363 views

### How can I export numerical data in a calculation-favorable format?

I am exporting some data into the txt file but since the values exported to this txt file expresses 10^6 to be *^6, I cannot use these numbers in calculations in other programs.. For instance, when I ...
777 views

### How to work with large numbers

How do I browse very large numbers in mathematica, say $10^{{10}^{{10}^{1.414\ldots}}}$? By browse I mean finding the $k$th decimal place before or after the decimal point. Everything I have tried ...
67 views

### Comparing large numbers [duplicate]

How can I compare really large numbers in Mathematica? I'm trying to compare: 2^4^4^4 < 4^4^4^4 It yields: ...
112 views

I'm using "mathlink.h" to call Mathematica from a C program. I send a computation to Mathematica and its return result is a very big number (100 digits). Hence, I want to read that number as a string. ...
624 views

### Strange behavior on very large numbers

I want to test the value of a differential equation by replacing a solution and setting random values for r and z variables: ...
365 views

### Can we compile using only Integers Of Unusual Size?

I coined Integers Of Unusual Size to mean "bignum" using GMP, the underpinning of Mathematica's ability to craft very big numbers. I have these functions from this question: ...
402 views

### What is the most efficient way to add zeros to end of a number?

Beside *10^n, is there a faster way to add thousands of zeros to end of a number? Updated Timings: ...