埃拉托色尼筛，生成素数。 循环问题

Question

I'm trying to generate n number of primes using the Sieve of Eratosthenes algorithm. I debugged it and saw that at some point it starts deleting numbers that had already been deleted. I can't what's the problem, but I can bet it's to do with my loops. Could you help pls?

import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Part6 {

    public static List<Integer> primeSequence(int n) {
        List<Integer> list = IntStream.range(2, n).boxed().collect(Collectors.toList());

        for (int i = 2; i <= list.size(); i++) {
            for (int j = i + 1; j <= list.size(); j++) {
            if(j % i == 0)
                list.remove(j);
            }
        }
       return  list;
        }


    public static void main(String[] args) {
        System.out.println(primeSequence(Integer.parseInt(args[0])));
    }
    
}

Answer 1

This is how Sieve of Eratosthenes works, it keeps marking all the multiples of prime numbers other than itself in the range.
For example, when we start with i=2 , we marks 4, 6, 8, 10, 12, ... as composite number.
Again for i=3 , it will mark 6, 9, 12, 15, ... as non-prime.
Please observe that 6 & 12 were marked twice. There are many more numbers which would be marked as composites multiple times. Hence this is normal.

Now, the above program has many issues as:

1. When you perform list.remove(j) , it actually removes the number at index j not the number j itself. So, to remove the composite number j we need to use Integer.valueOf(j)
2. Upper limit of the loops should not be list.size() as the size of list will keep decreasing as we keep removing the numbers. Hence, many numbers will be missed.

Below is the modified version of your code:

        for (int i = 2; i < n; i++)
        {
            for (int j = i + 1; j <= n; j++)
            {
                if (j % i == 0)
                {
                    list.remove(Integer.valueOf(j));
                }
            }
            System.out.println(list);
        }

Input: 100
Output:

[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]