hdu2138 How many prime numbers #include <bits/stdc++.h> using namespace std; typedef long long ll; ll prime[] = {,,,,}; ll qmul(ll a, ll b, ll mod) { ll res = ; while (b) { ) res = (res+a)%mod; a = (a+a)%mod; b >>= ; } return res; } ll qpow(ll…

题意:如果一个n位数恰好使用了1至n每个数字各一次,我们就称其为全数字的.例如,2143就是一个4位全数字数,同时它恰好也是一个素数. 最大的全数字的素数是多少? 思路: 最大全排列素数可以从 n = 9 使用 perv_permutation 倒序生成. 当 n = 9 或者 n = 8 时生成的全排列构成的数一定不是素数,因为它一定能被 3 整除,所以从 7 开始枚举. 因为生成的数字太大,所以采用米勒测试判断素数. /************************************…

传送门 miller−rabbinmiller-rabbinmiller−rabbin素数测试的模板题. 实际上miller−rabinmiller-rabinmiller−rabin就是利用费马小定理和二次探测的性质来进行判断的. 注意要多带几个素数进去判断(听大神说只要取遍了50以内的质数就可以判断intintint范围内的) 代码: #include<bits/stdc++.h> #define ri register int using namespace std; inline in…

来源: HDU 2007-11 Programming Contest_WarmUp 题目大意:素数判定. 思路: 事实上暴力判定也可以过,但我还是用了Miller-Rabin算法. 核心思想:利用费马小定理,得到对于质数$p$,我们有$a^{p-1}\equiv 1(mod\ p)$或$a^p\equiv a(mod\ p)$. 反过来,满足条件的不一定是质数,但有很大概率是质数,因此我们只要多随机几个$a$来判定,出错的概率就非常低了. 求幂的运算可以使用Montgomery模幂算法. 注意…

题目链接:http://acm.csu.edu.cn/csuoj/problemset/problem?pid=1552 Description On an alien planet, every extraterrestrial is born with a number. If the sum of two numbers is a prime number, then two extraterrestrials can be friends. But every extraterrestr…

Time Limit: 1000MS   Memory Limit: 65536K Description Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? For example, the integer 53 has two r…

题意: 欧拉发现了这个著名的二次多项式: f(n) = n2 + n + 41 对于连续的整数n从0到39,这个二次多项式生成了40个素数.然而,当n = 40时402 + 40 + 41 = 40(40 + 1) + 41能够被41整除,同时显然当n = 41时,412 + 41 + 41也能被41整除. 随后,另一个神奇的多项式n2 − 79n + 1601被发现了,对于连续的整数n从0到79,它生成了80个素数.这个多项式的系数-79和1601的乘积为-126479. 考虑以下形式的二次多…

Sum of Consecutive Prime Numbers Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 20050   Accepted: 10989 Description Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representatio…

题目链接: 传送门 Sum of Consecutive Prime Numbers Time Limit: 1000MS     Memory Limit: 65536K Description Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive intege…

Sieve of Eratosthenes (素数筛选算法) Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number. For example, if n is 10, the output should be “2, 3, 5, 7″. If n is 20, the output should be “2, 3, 5, 7, 11, 13,…