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.
55
questions
5
votes
2
answers
632
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Can I use NextPrime[n] up to n=10^14?
I would like to perform computations with primes up to $n=10^{14}$. To do so, I would like to go through all primes, from $2$ to $10^{14}$ and perform some calculation on each prime.
I saw that one ...
- 989
2
votes
1
answer
103
views
How can I make sure that the two given numbers are exactly the same?
I have the given numbers $n1$ and $n2$. How can I make sure that these two numbers are exactly the same? Numerically, using {N[n1,40], N[n2,40]}, by increasing the ...
- 361
13
votes
1
answer
225
views
Performance regression for big integer computation
Backslide introduced in 12.0, persisting through 13.1.
Recently I noticed that the big integer calculation of the new version is much slower than the old version, can you reproduce, is there a way to ...
- 5,562
3
votes
2
answers
105
views
Check certain expression using a while loop to run through all posibilities in a range
Well, I have written the following code (using the fast square root test found in this answer):
...
- 1,941
4
votes
3
answers
328
views
Checking if a number is right sorted
I have a number $n$ such that the digits of $n$ are strictly increasing to the left except for the first digit. So for example when $n=51369$ fits the bill because:
$$1<3<6<9\tag1$$
Is there ...
- 1,941
5
votes
8
answers
1k
views
Making the number 12345...n
Well, I am trying to write a code that makes the number:
$$123456\dots n\tag1$$
So, when $n=10$ we get:
$$12345678910$$
And when $n=15$ we get:
$$123456789101112131415$$
And when $n=4$ we get:
$$1234$$...
- 1,941
0
votes
1
answer
86
views
Parallelization in While[] loop when testing if a condition is met
Well, I am trying to run the following code:
...
- 1,941
1
vote
0
answers
110
views
Implementing the Binary GCD algorithm in Mathematica
Well, I have $n\in\mathbb{N}$ and I want to transform $n$ to a binary number which can be done using FromDigits[IntegerDigits[n, 2]]. I want to compute the ...
- 1,941
4
votes
3
answers
263
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Why $\pi$ // Rationalize does not give a rational multiple of $\pi$ in my example?
As an obvious example of π Rationalize, I see that
...
- 1,159
2
votes
1
answer
86
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How to write this simple task of unimodular prime search in mathematica?
For testing a particular algorithm I found mathematica is the best way as it has all the tools I need. I am stuck in a number theory part and since I am not an expert in mathematica I do not know how ...
- 145
1
vote
2
answers
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Filtering solutions in PowerRepresentations
I have the following code:
PowersRepresentations[10400, 7, 2]
This produces Length[PowersRepresentations[10400, 7, 2]]=433789 ...
- 1,941
2
votes
1
answer
97
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Help: Obtain a huge amount of data solved in FrobeniusSolve? (perhaps better without running FrobeniusSolve?) [closed]
How to obtain a huge amount of data solved in FrobeniusSolve more systematically?
I am interested in obtaining these two sets of data from FrobeniusSolve:
...
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1
vote
1
answer
96
views
1
vote
1
answer
264
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Using more than 6 kernels in ParallelTable function [duplicate]
I have the following code:
ParallelTable[
If[IntegerQ@Sqrt[80892036 + 17994 x (1 + x) (-5995 + 5998 x)], x,
Nothing], {x, 6694300, 31072325}]
It uses 6 ...
- 1,941
2
votes
1
answer
277
views
Using Parallelize in a solve function
Is there a way to use Parallelize the following operation, in order to make it do the calculations faster? Or is there another way to speed up this calculation?
...
- 1,941
3
votes
2
answers
223
views
Using the solve function for big numbers, getting a failure now
When I try to solve:
Solve[y^2==441+48*x*(1+x)(-13+16*x)&&1100*10^9<=y<=1200*10^9&&x>=2,{y,x},Integers]
My code runs for 169 seconds and ...
- 1,941
3
votes
1
answer
292
views
How to get the bit size (bit length) of an integer? [closed]
Suppose I have the integer 255, so 11111111 is its base 2 (bit) representation and the bit size of 255 is 8.
How can I calculate the bit size of a (big) integer in Mathematica?
Is there a built in ...
- 51
0
votes
0
answers
118
views
Sum of digits of large numbers with a particular form
I used Wolfram Alpha to find the sum of digits of these large numbers but the results are " standard computation time exceeded ". Could you help me because I want investigate these four numbers:
$((...
4
votes
3
answers
271
views
How to plot a function with huge numbers?
I have a huge polynomial function P which is dependent on x, I tried plotting the function but I am getting nothing in the plot. ...
- 1,699
2
votes
0
answers
173
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 ...
- 121
8
votes
2
answers
192
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:
<...
3
votes
3
answers
193
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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 ...
- 3,816
1
vote
1
answer
234
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 ...
- 161
1
vote
1
answer
59
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 ...
- 111
0
votes
0
answers
232
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 ...
- 101
6
votes
2
answers
922
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;...
- 3,603
0
votes
2
answers
535
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 ...
- 1
0
votes
0
answers
30
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];]
...
- 111
1
vote
2
answers
444
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 ...
- 111
3
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2
answers
209
views
6
votes
1
answer
130
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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 ...
- 329
10
votes
2
answers
526
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 ...
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11
votes
2
answers
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 ...
- 351
4
votes
1
answer
425
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 ...
- 49
2
votes
1
answer
103
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 ...
- 137
3
votes
1
answer
302
views
Datatypes and numbers in Mathematica
I have some questions about numbers in Mathematica:
Does Mathematica work with datatypes like int, long, ...
user29537
21
votes
1
answer
1k
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 ...
- 270k
4
votes
1
answer
289
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 ...
1
vote
1
answer
846
views
6
votes
4
answers
17k
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:
...
- 609
1
vote
3
answers
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
...
- 13
1
vote
1
answer
549
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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 ...
- 219
1
vote
0
answers
993
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 ...
1
vote
0
answers
77
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:
...
- 3,857
2
votes
1
answer
121
views
Read return value as string by Mathlink.h
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.
...
- 415
4
votes
1
answer
679
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:
...
- 1,911
6
votes
2
answers
444
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:
...
- 2,360
41
votes
1
answer
3k
views
4
votes
2
answers
710
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 ...
- 965
6
votes
2
answers
992
views
Fast Karatsuba Squaring, how to?
I want to improve timing of squaring for big numbers.
So I asked What is the fastest way to split a number into parts and What is the most efficient way to add zeros to end of a number with several ...
- 965