Primes.java

/*
 * A number is prime if it is not divisible by any number other than 1 and
 * itself. 1 is not prime. Thus you can test whether a number greater than 1 is
 * prime by checking whether it is divisible by any smaller number greater than
 * one.
 */

public class Primes {

  public boolean isPrime(int n) {
    for (int f = 2; f <= Math.sqrt(n); f++) {
      if (n % f == 0) return false;
    }
    return n != 1;
  }

  public int numberOfPrimesBelow(int bound) {
    int count = 0;
    for (int n = 2; n < bound; n++) {
      if (isPrime(n)) {
        count++;
      }
    }
    return count;
  }
}