Project Euler 97 ：Large non-Mersenne prime 非梅森大素数

Large non-Mersenne prime

The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 2^6972593−1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2^p−1, have been found which contain more digits.

However, in 2004 there was found a massive non-Mersenne prime which contains 2,357,207 digits: 28433×2^7830457+1.

Find the last ten digits of this prime number.

非梅森大素数

1999年人们发现了第一个超过一百万位的素数，这是一个梅森素数，可以表示为2^6972593−1，包含有2,098,960位数字。在此之后，更多形如2^p−1的梅森素数被发现，其位数也越来越多。

然而，在2004年，人们发现了一个巨大的非梅森素数，包含有2,357,207位数字：28433×2^7830457+1。

找出这个素数的最后十位数字。

解题

感觉很简单。。。

JAVA

package Level3;import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.math.BigInteger;
import java.util.ArrayList;public class PE097{public static void run() {BigInteger m = new BigInteger("10000000000");BigInteger r1 = new BigInteger("28433");BigInteger t = new BigInteger("2");BigInteger exp = new BigInteger("7830457");BigInteger res = t.modPow(exp, m);res = r1.multiply(res).add(new BigInteger("1"));res = res.mod(m);System.out.println(res);}public static void main(String[] args) throws IOException {long t0 = System.currentTimeMillis();run();long t1 = System.currentTimeMillis();long t = t1 - t0;System.out.println("running time="+t/1000+"s"+t%1000+"ms");}
}

// 8739992577
// running time=0s2ms

就这样

或者这样

    public static void run2(){long base = 2;long mod = 1000000000;long exp = 7830457;long res = 28433;for(long i =1;i<=exp;i++){res = (res*2)%mod;}res +=1;res %=mod;System.out.println(res);}
//    739992577
//    running time=0s163ms

上面mod少个0求的是后9位的数，因为多个0就越界了，少一位手工0到9可以暴力遍历。。。

Python

# coding=gbk
import copy
import time as time
def main():print ((28433*(2**7830457))+1)%10000000000
t0 = time.time()
main()
t1 = time.time()
print "running time=",(t1-t0),"s"
# 8739992577
# running time= 0.0190000534058 s

也就这样

转载于:https://www.cnblogs.com/theskulls/p/5024164.html

Project Euler 97 ：Large non-Mersenne prime 非梅森大素数相关推荐

Project Euler 3 Largest prime factor
Project Euler 3 Largest prime factor ''' The prime factors of 13195 are 5, 7, 13 and 29. What is the ...
[Project Euler] 来做欧拉项目练习题吧: 题目012
[Project Euler] 来做欧拉项目练习题吧: 题目012 周银辉问题描述: The sequence of triangle numbers is generated by addin ...
欧拉计划(project euler)最详细中文题解
欧拉计划是一个在线解题网站,题目以各类数学问题为主,通常需要结合一定的数学与编程知识,写出适当的程序求解问题(详细介绍可以参见我的文章).相比于力扣等刷题网站,欧拉计划上的题目有着更丰富的知识背景,在 ...
欧拉计划 Project Euler 50-56
Project Euler 50-56 Project Euler: https://projecteuler.net/ Project Euler | 欧拉计划: https://pe-cn.git ...
【AlgorithmTraining】03：Project Euler 03
Project Euler 03 OVERVIEW Project Euler 03 1.E22:Name score 2.E32:Pandigital products 3.E33:Digit ca ...
硬币游戏 Project Euler 232
原帖:http://hi.baidu.com/atyuwen/blog/item/160bd024531e3034c995591d.html Project Euler上最近的题目都还比较意思,来看看 ...
[Project Euler] 来做欧拉项目练习题吧: 题目004
[Project Euler] 来做欧拉项目练习题吧: 题目004 周银辉问题描述: A palindromic number reads the same both ways. The l ...
[Project Euler] 来做欧拉项目练习题吧: 题目017
[Project Euler] 来做欧拉项目练习题吧: 题目017 周银辉题目描述: If the numbers 1 to 5 are written out in words: one, two ...
Project Euler
最近发现了一个很有趣的网站,Project Euler 上面全是数学题,不过大多需要用编程解决 Problem 3: 求:600851475143的最大素因子. 解:编了个程序,迅速水过,看官方的题解 ...

Project Euler 97 ：Large non-Mersenne prime 非梅森大素数

Project Euler 97 ：Large non-Mersenne prime 非梅森大素数相关推荐

最新文章

热门文章