Starting with n True values in an array, with i enumerated from 3 to sqrt(n) by the step of 2, if the ith entry in the array is still True, set to False all entries from i^2 to the end of the array by the step of 2*i (these all will be multiples of i).
All odd True entries above 1 that are left in the array in the end, are prime.
All thus found numbers, and 2, are all the prime numbers that exist below n.