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/*

* 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

}

}

}