Tagged Questions

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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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 ...
956 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 ...
208 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 ...
72 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 ...
128 views

Datatypes and numbers in Mathematica

I have some questions about numbers in Mathematica: Does Mathematica work with datatypes like int, long, ...
460 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 ...
193 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 ...
187 views

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

I'm trying to run this ...
4k 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: ...
292 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 ...
106 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 ...
255 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 ...
55 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: ...
96 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. ...
351 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: ...
269 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: ...
1k views

How to compare power towers in Mathematica?

First I tried it directly, but it overflowed: ...
495 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 ...
536 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 ...
378 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: ...
969 views

Mathematica output format for big numbers

I need to write output of a Mathematica expression (a list of equations) in a file. I use ...
4k 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: ...