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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 single question. As long as you can guide me or where I can get this information on my own, I will consider my question answered.

Let's start with the first round of questions:

  1. How do I know the limit of digits Wolfram can manipulate?
  2. Does this limit depend on the available memory?
  3. Can I set this limit? (and how to do it, of course)
  4. If I exceed this limit by half the algorithm, does Wolfram warn me?
  5. And if it doesn't, then I would like to know what to do to detect that my algorithm is out of control.

I also work with various number-theoretic functions. Here's the second round of questions:

  1. Do these functions also have a limit?
  2. Is this limit independent of the maximum number of digits Wolfram can manipulate?
  3. And I would also like to know how to detect that a function cannot process such big integers.

I think my problem is that I don't quite understand how Wolfram manipulates integer numbers.

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closed as too broad by m_goldberg, MarcoB, Sektor, halirutan, Michael E2 May 26 '18 at 20:54

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This question is unfortunately much too broad and I'm voting to close it in its current form. However, I'd like to say two things: (1) Working with integers is usually only restricted by your RAM but (2) certain functions that appear to be integer functions might use some numerical approximation in the background that is not obvious. $\endgroup$ – halirutan May 25 '18 at 20:38