Problem 7 of What is the 10 001st prime number?

本文介绍了一个Java程序,该程序用于找出第10001个质数。通过遍历数字并使用isPrime方法检查每个数字是否为质数,最终确定了目标质数为104743。

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

public class BigPrime {
	public static void main(String args[]){
		int j=0;
		for(long i=2;i<2000000000;i++){
			if(isPrime(i)){
				j++;
				if(j==10001){
					System.out.println(i);
				}
			}
		}
	}
	
	public static boolean isPrime(long n){
	    for(int i = 2; i * i <= n; i++){
	  if(n % i == 0)
	   return false;
	  }
	    return true;
	}
}

Answer:
104743

A-1 Intersection Set of Prime Factors 分数 20 作者 陈越 单位 浙江大学 Given a positive integer n. Select two distinct digits from the decimal repersentation(十进制表示)of n, we obtain another integer m. What is the size of the intersection set(交集)of the prime factors of n and m? For example, given n=623457198, its prime factor set is A = {2, 3, 7, 13, 380621}. Swapping 2 and 9 gives us m=693457128, of which the prime factor set is B = {2, 3, 7, 13, 109, 971}. Then the intersection set of A and B is {2, 3, 7, 13}, with 4 factors. Input Specification: Each input file contains one test case, which gives a positive integer n (10<n≤10 9 ). It is guaranteed that there are at least 2 distinct digits in n. Output Specification: Swap any pair of digits in n to obtain m, you are supposed to find the m with the largest intersection set of the prime factors of n and m. Output in a line the number of the prime factors in the intersection set, together with m. The numbers must be separated by 1 space, and there must be no extra space at the beginning or the end of the line. In case such an m is not unique, output the one with the smallest value. Sample Input: 623457198 Sample Output: 4 123457698 Hint: There are two m's with 4 common factors. Besides the one given in the problem description, we can also swap 6 and 1 to obtain 123457698. This number has a prime factor set {2, 3, 7, 13, 23, 29, 113}, and so the intersection set is also {2, 3, 7, 13}. This number is in the ouput because it is smaller than 693457128.(c++)
最新发布
07-28
评论
成就一亿技术人!
拼手气红包6.0元
还能输入1000个字符
 
红包 添加红包
表情包 插入表情
 条评论被折叠 查看
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值