PrimeNumberOptimalApproach.java

/**
    @author wasitshafi
    @since  18-02-2020
*/
import java.util.TreeSet;
public class PrimeNumberOptimalApproach
{
    public static boolean isPrime(int n)
    {
        for(int i = 2 ; i * i <= n ; i++)
            if(n % i == 0)
                return false;
        return true;
    }
    public static void main(String... args)
    {
        int n = Integer.MAX_VALUE, j;
        TreeSet<Integer> primes = new TreeSet<>();
        TreeSet<Integer> primes2 = new TreeSet<>();
        TreeSet<Integer> primes3 = new TreeSet<>();
        n = 1000000; // because i was getting out of memory on my PC, although it worked fine for large number on our computer lab Desktop Workstations

        // refer online : https://www.free-online-calculator-use.com/prime-number-generator.html
        //n = 104730; 
        
        // Method1
        loop:for(int i = 2 ; i <= n ; i++)
        {
            for(j = 2 ; j * j <= i ; j++)
                if(i % j == 0) continue loop;
            primes.add(i);
        }        

        // Method2
        primes2.add(2);
        primes2.add(3);
        primes2.add(5);
        loop2:for(int i = 5 ; i <= n ; i++)
        {
            if(i % 2 == 0 || i % 3 == 0 || i % 5 == 0) continue loop2;
            for(j = 1 ; 6 * j - 1 <= Math.sqrt(i) ; j++)
            {
                if(i % (6 * j - 1) == 0) continue loop2;
                if(6 * j + 1 <= Math.sqrt(i)) if(i % (6 * j + 1)  == 0) continue loop2;
            }
            primes2.add(i);
        }

        //Method2.1
        primes3.add(2);
        primes3.add(3);
        primes3.add(5);
        loop2:for(int i = 5 ; i <= n ; i++)
        {
            if(i % 2 == 0 || i % 3 == 0 || i % 5 == 0) continue loop2;
            for(j = 1 ; 6 * j - 1 <= Math.sqrt(i) ; j++)
            {
                if(isPrime(6 * j - 1))
                {
                    if(i % (6 * j - 1) == 0) continue loop2;
                }
                if(isPrime(6 * j + 1))
                {
                    if(6 * j + 1 <= Math.sqrt(i)) if(i % (6 * j + 1)  == 0) continue loop2;
                }
            }
            primes3.add(i);
        }
        //System.out.println();
        //System.out.println("primes  : " + primes);
        //System.out.println("primes2 : " + primes2);
        //System.out.println("primes3 : " + primes3);
        System.out.println("|primes|  : " + primes.size());
        System.out.println("|primes2| : " + primes2.size());
        System.out.println("|primes3| : " + primes3.size());
        System.out.println("Primes.equals(Primes2)  : " + primes.equals(primes2));
        System.out.println("Primes2.equals(Primes3) : " + primes2.equals(primes3));
    }
}