Java prints all prime numbers within N

Question:

Print out all prime numbers within N

(Video tutorial sharing: java course)

Idea:

The definition of a prime number is that its factors are only 1 and itself, so when we judge, we can judge based on whether the number traversed has factors other than 1 and itself. At the same time, we know that if there is a factor (that is, if it is a composite number), then the factor must be smaller than this number, and we will eliminate it.

Code implementation:

package Algorithm.Interview;

import java.util.ArrayList;
import java.util.List;

public class primeNum {
    public List<Integer> PrintPrime(int n){
        List<Integer> Prime = new ArrayList<>();
        //2也是质数
        Prime.add(2);
        //外循环遍历N以内的所有数，1不是质数，2是质数，所以从2开始遍历
        for (int i = 2; i <= n; i++) {
        //内循环遍历小于要判断的数的因子，即要判断的数是否有除了1和它本身的因子
            for (int j = 2; j < i; j++) {
            	//如果有因子，直接跳出内循环，到外循环遍历下一个数
                if (i % j == 0){
                    break;
                }
                //如果没有因子，判断j = i-1这个数，能循环到i-1说明之前的j都没有跳出循环，来判断最后一个小于i的数是不是i的因子
                else if (j == i -1 && i % j != 0){
                    Prime.add(i);
                }
            }

        }
        return Prime;
    }

    public static void main(String[] args) {
        primeNum primeNum = new primeNum();
        System.out.println(primeNum.PrintPrime(100));
    }
}

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