(Revise Listing 1, PrimeNumber.java) Listing 1 determines whether a number n is prime by c...

(Revise Listing 1, PrimeNumber.java) Listing 1 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 2n can divide n evenly. If not, n is prime. Rewrite Listing 1 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.

LISTING 1 PrimeNumber.java

1 public class PrimeNumber {
2 public static void main(String[] args) {
3 final int NUMBER_OF_PRIMES = 50; // Number of primes to display
4 final int NUMBER_OF_PRIMES_PER_LINE = 10; // Display 10 per line
5 int count = 0; // Count the number of prime numbers
6 int number = 2; // A number to be tested for primeness
7
8 System.out.println("The first 50 prime numbers are \n");
9
10 // Repeatedly find prime numbers
11 while (count
12 // Assume the number is prime
13 boolean isPrime = true; // Is the current number prime?
14
15 // Test whether number is prime
16 for (int divisor = 2; divisor <= number / 2; divisor++) {
17 if (number % divisor == 0) { // If true, number is not prime
18 isPrime = false; // Set isPrime to false
19 break; // Exit the for loop
20 }
21 }
22
23 // Display the prime number and increase the count
24 if (isPrime) {
25 count++; // Increase the count
26
27 if (count % NUMBER_OF_PRIMES_PER_LINE == 0) {
28 // Display the number and advance to the new line
29 System.out.println(number);
30 }
31 else
32 System.out.print(number + " ");
33 }
34
35 // Check if the next number is prime
36 number++;
37 }
38 }
39 }