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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6
votes
2answers
859 views

Number of digits for factorial of 12345678987654321

A hard math problem 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 ...
4
votes
1answer
198 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 ...
1
vote
1answer
64 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 ...
2
votes
1answer
109 views

Datatypes and numbers in Mathematica

I have some questions about numbers in Mathematica: Does Mathematica work with datatypes like int, long, ...
19
votes
1answer
408 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 ...
4
votes
1answer
189 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 ...
-1
votes
1answer
157 views
4
votes
2answers
2k 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: ...
1
vote
3answers
218 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 ...
1
vote
1answer
97 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 ...
1
vote
0answers
194 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
0answers
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: ...
2
votes
1answer
94 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. ...
4
votes
1answer
311 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: ...
6
votes
2answers
251 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: ...
39
votes
1answer
1k views

How to compare power towers in Mathematica?

First I tried it directly, but it overflowed: ...
4
votes
2answers
480 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 ...
5
votes
2answers
502 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 ...
4
votes
2answers
375 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: ...
4
votes
2answers
924 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 ...
48
votes
2answers
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: ...
21
votes
8answers
3k 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 ...
12
votes
2answers
361 views

What determines the value of $MaxNumber?

What determines the value of $MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ...