Are You A Prime Number

Question

I\'ve been interested in the problem of finding a better prime number recognizer for years. I realize this is a huge area of academic research and study - my interest in this i

Answer 1

You can make small cuts to your algorithm without adding too much code complexity. For example, you can skip the even numbers on your verification, and stop the search as soon as you find a factor.

if (input < 2 || (input != 2 && input % 2 == 0))
  factorFound = 1;

if (input > 3)
  for (i = 3; i <= ceiling && !factorFound; i += 2)
    if (input % i == 0)
      factorFound = 1;

Regarding the complexity, if n is your input number, wouldn't the complexity be O(sqrt(n)), as you are doing roughly at most sqrt(n) divisions and comparisons?