Chapter 7 Exercise 6, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

*7.6 (Revise Listing 5.15, PrimeNumber.java) Listing 5.15 determines whether a number n is prime by checking whether 2, 3, 4, 5, 6, . . . , n/2 is a divisor. If a divisor is found, n is not prime. A more efficient approach is to check whether any of the prime numbers less than or equal to $\sqrt{n}$ can divide n evenly. If not, n is prime. Rewrite Listing 5.15 to display the first 50 prime numbers using this approach. You need to use an array to store the prime numbers and later use them to check whether they are possible divisors for n.

public class ProgrammingEx7_6 {
 public static void main(String[] args) {
  final int NUMBER_OF_PRIMES = 50; // Number of primes to display
  final int NUMBER_OF_PRIMES_PER_LINE = 10; // Display 10 per line
  int[] numbers = { 2 }; // First prime
  int number = 2; //Start testing for prime at 2
 
  System.out.println("The first 50 prime numbers are \n");
 
  // Repeatedly find prime numbers
  while (numbers.length<= NUMBER_OF_PRIMES) {
   // Assume the number is prime
   boolean isPrime = true; // Is the current number prime?
 
   // Test if number is prime
   for (int i = 0; i < numbers.length && numbers[i]< Math.sqrt(number); i++) {
    int divisor = numbers[i];
    if (number % divisor == 0) { // If true, number is not prime
     isPrime = false; // Set isPrime to false
     break; // Exit the for loop
    }
   }
 
   // Add the prime number to array
   if (isPrime) {
    numbers= add2Array(numbers, number);
 
    if ((numbers.length-1) % NUMBER_OF_PRIMES_PER_LINE == 0) {
     // Print the number and advance to the new line
     System.out.println(number);
    } else
     System.out.print(number + " ");
   }
 
   // Check if the next number is prime
   number++;
  }
 }
 
 // Copy array numbers1 to array numbers2
 // If the length of array numbers2 is less then array numbers2, return false
 public static boolean copyArray(int[] source, int[] dest) {
  if (source.length > dest.length)
   return false;
 
  for (int i = 0; i < source.length; i++) {
   dest[i] = source[i];
  }
  return true;
 }
 
 // Increase array size by one and add integer to the end of array
 // Return new array
 public static int[] add2Array(int[] source, int data) {
 
  int[] dest = new int[source.length + 1];
  copyArray(source, dest);
  dest[source.length] = data;
  return dest;
 
 }
}