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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42
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 : ...
38
votes
1answer
1k views

How to compare power towers in Mathematica?

First I tried it directly, but it overflowed: ...
19
votes
1answer
327 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 ...
17
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
341 views

What determines the value of $MaxNumber?

What determines the value of $MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ...
6
votes
2answers
220 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: ...
5
votes
2answers
455 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
1answer
262 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: ...
4
votes
2answers
368 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
871 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 ...
3
votes
2answers
1k 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: ...
3
votes
1answer
167 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 ...
3
votes
2answers
459 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 ...
2
votes
1answer
91 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. ...
1
vote
3answers
141 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
89 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
138 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: ...
0
votes
0answers
7 views

What's the last whole number before a googolplex? [migrated]

"What's the last whole number before a googolplex?" My six yr old asked me this, this evening, how does a math challenged dad answer this?! A googolplex is hard enough as it is to imagine or ...
-1
votes
1answer
89 views