Talk:Prime number

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Primality testing - Problems with the number 4

When testing whether a number N is divisible by s, using values of s from 2 to N - 1, when N is 4, the method correctly determines that 4 is not prime, because it is divisible by 2. This example is in the C programming language.

for (s = 2; s < N - 1; ++s) {
   if (N % s == 0) {
      printf("N is not a prime number.");
   }
}

However, when using values of m from 2 to the square root of n, when n is 4, an error can occur. Since 2 is the square root of 4, the test range is 2 to 2, and, if the range is exclusive, as in a for-loop, the whole test is skipped, and 4 is incorrectly determined to be a prime number.

for (s = 2; s < sqrt(N); ++s) {
   if (N % s == 0) {
      printf("N is not a prime number.");
   }
}

Isaac4given 11:28, 10 January 2008 (EST)