Merge pull request #5 from RianGallagher/master

Added Sieve of Eratosthenes algorithm for finding primes

FindingPrimes.java

@@ -0,0 +1,30 @@
+/*
+ * 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
+		}
+	}
+}