Return all prime numbers smaller than M

Question

Given an integer M. return all prime numbers smaller than M.

Give a algorithm as good as you can. Need to consider time and space complexity.

Answer 1

You can do it using a bottom up dynamic programming approach called the Sieve of Eratosthenes Basically you create a boolean cache of all numbers upto n and you mark each the multiples of each number as not_prime. Further optimizations can be gained by checking only upto sqrt(n) since any composite number will have at least one divisor less that sqrt(n)

    public int countPrimes(int n) {
    if(n==0){
        return 0;
    }else{
        boolean[] isPrime=new boolean[n];
        for(int i=2;i