The Sieve of Eratosthenes You can find all the prime numbers very quickly by using a strategy called The Sieve of Eratosthenes. You use an array and nested loops to do this. First declare an array of int for 10000 elements. Put 0 into all the places (should automatically put in 0's but check) Put 1's into all the multiples of 2 - a[4] a[6] a[8] etc. (Note not a[2]) Put 1's into all the multiples of 3 - a[6] a[9] a[12] etc. (Note not a[3]) You don't have to put 1's into multiples of 4 since a[4] is already 1 Put 1's into all the multiples of 5 - a[10] a[15] a[20] etc. (Note not a[5]) Continue this until you reach 1/2 the array size. When you are done - go through the array and anywhere you find a 0 print out that subscript. Since a[1] is holding a 0 print out the 1. Since a[2] is holding a 0 print out the 2. Since a[3] is holding a 0 print out the 3. Since a[4] is holding a 1 do not print out the 4.