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  • Dirichlet's Theorem on Arithmetic Progressions

    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 by d.

    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

    92809
    6709
    12037
    103
    93523
    14503
    2
    899429
    5107
    412717
    22699
    25673
    
    
    
    #include <iostream>
    #include <cmath>
    using namespace std;
    int main()
    {int i,j,b;
    	int a1,a2,a3,a,k;
    	while(cin>>a1>>a2>>a3&&a1!=0)
    	{k=0;i=0;j=0;i=0;
    		while(i<a3)
    	{
    	bool l=0;
    		a=a1+a2*k;
    for(j=2;j<=sqrt(a);j++)
    if(a%j==0&&a!=2)
    {l=1;break;}
    if(l==0&&a>1)
    {b=a;
    i++;}
    k++;
    		}
    cout<<b<<endl;
    
    }
    return 0;
    
    
    }
     

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  • 原文地址:https://www.cnblogs.com/lengxia/p/4387850.html
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