Sieve of Eratosthenes
Steve of Eratosthenes is an ancient and very important algorithm for finding all primes number up to a given limit. this algorithm is named after great Greek mathematician “ Eratosthenes”. Principle of Steve of Eratosthenes algorithm is removing all prime numbers i.e. composite numbers from array and now remaining numbers are Prime numbers. For more about algorithm go to Wikipedia . Now without wasting your time I like discuss steps for Steve of Eratosthenes and a simple code in Java to find all prime numbers up to a limit. Algorithm : Step 1: Make an array from 2 to n [2 , 3 , 4 , 5 , 6 , 7 ,8 , 9 ,........ n] Step 2: Beginnings from 2 delete all of its multipliers in the array except itself. for 2 [2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ,......n] Step 3: Repeat the step 2 till square root of n. for 3 [2 ,3 , 5 , 7 , 9 , ............ n] . . . . Repeat till sqrt(n) Source Code import java.util.*; public class SteveOfEratosthenes { pu