FindingPrimes.java

/*
 * The Sieve of Eratosthenes is an algorithm used to find prime numbers, up to a given value.
 * Illustration: https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
*/
public class FindingPrimes{
	public static void main(String args[]){
		SOE(20); //Example: Finds all the primes up to 20
	}

	public static void SOE(int n){
		boolean sieve[] = new boolean[n];

		int check = (int)Math.round(Math.sqrt(n)); //No need to check for multiples past the square root of n

		sieve[0] = false;
		sieve[1] = false;
		for(int i = 2; i < n; i++)
			sieve[i] = true; //Set every index to true except index 0 and 1

		for(int i = 2; i< check; i++){
			if(sieve[i]==true)					//If i is a prime
				for(int j = i+i; j < n; j+=i)   //Step through the array in increments of i(the multiples of the prime)
					sieve[j] = false;			//Set every multiple of i to false
		}
		for(int i = 0; i< n; i++){
			if(sieve[i]==true)
				System.out.print(i+" "); //In this example it will print 2 3 5 7 11 13 17 19
		}
	}
}