狄利克雷定理与素数求解-优快云博客

本文链接：https://blog.youkuaiyun.com/acm_xmzhou/article/details/11746225

Dirichlet's Theorem on Arithmetic Progressions

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 14181		Accepted: 7089

Description

If a and d are relatively prime positive integers, the arithmetic sequence beginning with a and increasing by d, i.e., a, a + d, a + 2d, a + 3d, a + 4d, ..., contains infinitely many prime numbers. This fact is known as Dirichlet's Theorem on Arithmetic Progressions, which had been conjectured by Johann Carl Friedrich Gauss (1777 - 1855) and was proved by Johann Peter Gustav Lejeune Dirichlet (1805 - 1859) in 1837.

For example, the arithmetic sequence beginning with 2 and increasing by 3, i.e.,

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, ... ,

contains infinitely many prime numbers

2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, ... .

Your mission, should you decide to accept it, is to write a program to find the nth prime number in this arithmetic sequence for given positive integers a, d, and n.

Input

The input is a sequence of datasets. A dataset is a line containing three positive integers a, d, and n separated by a space. a and d are relatively prime. You may assume a <= 9307, d <= 346, and n <= 210.

The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset.

Output

The output should be composed of as many lines as the number of the input datasets. Each line should contain a single integer and should never contain extra characters.

The output integer corresponding to a dataset a, d, n should be the nth prime number among those contained in the arithmetic sequence beginning with a and increasing byd.

FYI, it is known that the result is always less than 10⁶ (one million) under this input condition.

Sample Input

367 186 151
179 10 203
271 37 39
103 230 1
27 104 185
253 50 85
1 1 1
9075 337 210
307 24 79
331 221 177
259 170 40
269 58 102
0 0 0

Sample Output

Source

Japan 2006 Domestic

这道题倒是没啥可说的，唯一要注意的就是打素数表一定要用筛法！！

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <map>
#include <string>
#include <stack>
#include <cctype>
#include <vector>
#include <queue>
#include <set>
#include <utility>
#include <cassert>
using namespace std;
///#define Online_Judge
#define outstars cout << "***********************" << endl;
#define clr(a,b) memset(a,b,sizeof(a))
#define lson l , m  , rt << 1
#define rson m + 1 , r , rt << 1 | 1
#define mk make_pair
#define FOR(i , x , n) for(int i = (x) ; i < (n) ; i++)
#define FORR(i , x , n) for(int i = (x) ; i <= (n) ; i++)
#define REP(i , x , n) for(int i = (x) ; i > (n) ; i--)
#define REPP(i ,x , n) for(int i = (x) ; i >= (n) ; i--)
const int MAXN = 1000000 + 500;
const int sigma_size = 26;
const long long LLMAX = 0x7fffffffffffffffLL;
const long long LLMIN = 0x8000000000000000LL;
const int INF = 0x7fffffff;
const int IMIN = 0x80000000;
#define eps 1e-8
const int MOD = (int)1e9 + 7;
typedef long long LL;
const double PI = acos(-1.0);
typedef double D;
typedef pair<int , int> pi;
///#pragma comment(linker, "/STACK:102400000,102400000")
int a[MAXN];
void prime_table()
{
    a[0] = a[1] = 0;
    FORR(i , 2 , MAXN)a[i] = 1;
    FORR(i , 2 , MAXN)
    {
        if(a[i])
        {
            for(int j = 2 * i ; j <= MAXN ; j += i)
            {
                a[j] = 0;
            }
        }

    }
}
int main()
{
//    freopen("heritage.in","r",stdin);
//    freopen("heritage.out","w",stdout);
    int aa , d ,n;
    prime_table();
//    FOR(i , 2 , 100)cout << a[i] << ' ';
    while(~scanf("%d%d%d", &aa,  &d , &n) && (aa || d || n))
    {
//        cout << d << endl;
        while(n)
        {
//            outstars
//            cout << aa << endl;
            if(a[aa])n--;
            aa += d;
        }
        printf("%d\n" , aa - d);
    }
    return 0;
}

！

POJ 3006