[Sieve of Eratosthenes]埃拉托色尼素数筛选法

In mathematics, the Sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους) is a simple, ancient algorithm for finding all prime numbers up to a specified integer.[1] It works efficiently for the smaller primes (below 10 million).[2] It was created by Eratosthenes, an ancient Greek mathematician. However, none of his mathematical works survived—the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus.

A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself.

[素数的定义是,一个仅能被1和本身整除的自然数]

To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method:

[可以通过以下的埃拉托色尼筛选法寻求所有小于整数n的素数]

Create a list of consecutive integers from two to n: (2, 3, 4, ..., n). [列出从2到n的一串连续自然数]
Initially, let p equal 2, the first prime number. [开始,先把2当作第一个素数,并赋值给变量p]
Strike from the list all multiples of p less than or equal to n. (2p, 3p, 4p, etc.) [将该列自然数中划掉p的倍数]
Find the first number remaining on the list after p (this number is the next prime); replace p with this number. [将剩下的自然数按原来顺序重新组成新的一列,并将第一个数赋给变量p]
Repeat steps 3 and 4 until p2 is greater than n. [重复第三第四步,直到p的平方大于n]
All the remaining numbers in the list are prime. [剩下的自然数就是所有小于n的素数]

	public static List<Long> find_prime_below_number(long number){
		int exe_number = 0;
		boolean close = false;
		List<Long> numberSet = new ArrayList<Long>();
		List<Long> resultSet = new ArrayList<Long>();
		
		for(long i=3; i<number; i+=2){
			numberSet.add(i);
			exe_number++;
		}
		double half = Math.sqrt(number);
		do{
			Long curN = numberSet.get(0);
			resultSet.add(curN);
			for(int j=0; j<numberSet.size(); j++){
				exe_number++;
				long l = numberSet.get(j);
				if(l%curN==0){
					numberSet.remove(j);
				}
			}
			if(curN>half){
				close = true;
			}
		}while(!close&&numberSet.size()!=0);
		
		if(numberSet.size()!=0){
			for(Long n : numberSet){
				exe_number++;
				resultSet.add(n);
			}
		}
		System.out.println("exe_number:"+exe_number);
		return resultSet;
	}

当找1000000以下的素数时，执行就挂了
肯定有问题
因为原算法说了是10 million
以下的数字~
一千万以下啊~
想办法解决