The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? #include<stdio.h> #include<string.h> #include<math.h> #include<ctype.h> #include<stdlib.h> #include<stdbool.h>…

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime. What is the largest n-digit pandigital prime that exists? 题目大意: 如果一个数字将1到n的每个数字都使用且只…

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? 翻译过后如下: 找出一个合数的最大质数因子 13195的质数因子有5,7,13和29. 600851475143的最大质数因子是多少? 做出答案以后的题解: 对于给定的n, 使factor = 2, 3, 4, 5, 6..., 对于每个factor, 当factor能被n完全整…

题目描述: 源码: 需要注意,若使用cin,cout输入输出,会超时. #include"iostream" #include"memory.h" #define MAX 1000000 using namespace std; int index[MAX]; int main() { memset(index, -1, sizeof(index)); index[1] = 0; int sum = 0; for(int i = 2; i < MAX; i++…

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? #include <stdio.h> #include <string.h> #include <ctype.h> #include <math.h> int prim(int n) { i…

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91  99. Find the largest palindrome made from the product of two 3-digit numbers. #include<stdio.h> #include<math.h> #…

problem 3:Largest prime factor 题意:求600851475143的最大的质因数 代码如下: #ifndef PRO3_H_INCLUDED #define PRO3_H_INCLUDED #include "prime.h" namespace pro3{ long long solve(){ ;; ;i*i<=n;++i) ){ if(isPrime(n/i))return n/i; else if(isPrime(i))maxn=i; } >…

Largest prime factor Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 13481    Accepted Submission(s): 4765 Problem Description Everybody knows any number can be combined by the prime number.Now,…

1. 问题: The prime factors of 13195 are 5, 7, 13 and 29.What is the largest prime factor of the number 600851475143 ? 2. 解法(by java in Eclipse) package com.lun.alrithmetic; /* * Q1: what's the primary factor? (1 2 3) * Q2: i & i+2ne能否遍历出所有质数 */ public…

Problem Description Everybody knows any number can be combined by the prime number.Now, your task is telling me what position of the largest prime factor.The position of prime 2 is 1, prime 3 is 2, and prime 5 is 3, etc.Specially, LPF(1) = 0.   Input…

The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another. There are no arithmetic seq…

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? 欧拉题里很多是关于求质数,求质数的方法很多,我推荐的是筛选法,效率高,也很好理解.百度一下就有详细说明. def primeslist(max): a = [True]*(max+1) # 创建一个list,下标的位置就代表数字 a[0],a[1]=False,False # 0…

Problem Description Everybody knows any number can be combined by the prime number. Now, your task is telling me what position of the largest prime factor. The position of prime 2 is 1, prime 3 is 2, and prime 5 is 3, etc. Specially, LPF(1) = 0. Inpu…

Largest prime factor Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 6990    Accepted Submission(s): 2471 Problem Description Everybody knows any number can be combined by the prime number. Now…

Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relative…

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. 9 = 7 + 21215 = 7 + 22221 = 3 + 23225 = 7 + 23227 = 19 + 22233 = 31 + 212 It turns out that the conjecture was false. What…

The first two consecutive numbers to have two distinct prime factors are: 14 = 2  7 15 = 3  5 The first three consecutive numbers to have three distinct prime factors are: 644 = 2²  7  23 645 = 3  5  43 646 = 2  17  19. Find the first four consecutiv…

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3. Fi…

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97. How many circular primes are there…

Problem Description Everybody knows any number can be combined by the prime number. Now, your task is telling me what position of the largest prime factor. The position of prime 2 is 1, prime 3 is 2, and prime 5 is 3, etc. Specially, LPF(1) = 0. Inpu…

Consider the fraction, n/d, where n and d are positive integers. If nd and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d  8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1…

The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... By converting each letter in a word to a number corresponding to its alphabetical position and…

The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145: 1! + 4! + 5! = 1 + 24 + 120 = 145 Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it tu…

Consider the fraction, n/d, where n and d are positive integers. If nd and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d  8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1…

There are exactly ten ways of selecting three from five, 12345: 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345 In combinatorics, we use the notation, 5C3 = 10. In general, It is not until n = 23, that a value exceeds one-million: 23C10 = 114406…

The decimal number, 585 = 10010010012(binary), is palindromic in both bases. Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2. (Please note that the palindromic number, in either base, may not include le…

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. Find the sum of all numbers which are equal to the sum of the factorial of their digits. Note: as 1! = 1 and 2! = 2 are not sums they are not included. 题目大意: 145 是一个奇怪的数字, 因为 1! + 4! + 5!…

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that49/98 = 4/8, which is correct, is obtained by cancelling the 9s. We shall consider fractions like, 30/50 = 3/5, to be…

Consider all integer combinations ofabfor 2a5 and 2b5: 22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024 52=25, 53=125, 54=625, 55=3125 If they are then placed in numerical order, with any repeats removed, we get the f…

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 21 22 23 24 2520  7   8   9  1019  6   1   2  1118  5   4   3  1217 16 15 14 13 It can be verified that the sum of the numbers on the di…