Question

This small C script checks if a number is a prime… Unfortunately it doesn’t fully work. I am aware of the inefficiency of the script (e.g. sqrt optimization), these are not the problem.

#include <stdio.h>

int main() {
  int n, m;

  printf("Enter an integer, that will be checked:\n"); // Set 'n' from commandline
  scanf("%d", &n); // Set 'n' from commandline

  //n = 5; // To specify 'n' inside code.

  for (m = n-1; m >= 1; m--) {
    if (m == 1) {
      printf("The entered integer IS a prime.\n");
      break;
    }
    if (n % m == 0) {
      printf("The entered integer IS NOT a prime.\n");
      break;
    }
  }
  return 0;
}

I tested the programm with a lot of numbers and it worked… Then I tried a bigger number (1231231231231236) which is clearly not a prime…
BUT: the program told me it was!?

What am I missing…?

Answer 1

The number “1231231231231236” is too big to fit in an “int” data type. Add a printf statement to show what number your program thinks you gave it, and if that’s prime, your program works fine; else, you might have a problem that merits checking. Adding support for integers of arbitary size requires considerable extra effort.

The reason you are having this problem is that intrinsic data types like int have a fixed size – probably 32 bits, or 4 bytes, for int. Given that, variables of type int can only represent 2^32 unique values – about 4 billion. Even if you were using unsigned int (you’re not), the int type couldn’t be used to store numbers bigger than around 4 billion. Your number is several orders of magnitude larger than that and, as such, when you try to put your input into the int variable, something happens, but I can tell you what doesn’t happen: it doesn’t get assigned the value 1231231231231236.