文章标题 CoderForces 755A : PolandBall and Hypothesis(水)
2017-01-16 13:04
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PolandBall and Hypothesis
PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: “There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number”.Unfortunately, PolandBall is not experienced yet and doesn’t know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.
Input
The only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall’s hypothesis.
Output
Output such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 103. It is guaranteed the the answer exists.
Examples
input
3
output
1
input
4
output
2
Note
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.
For the first sample testcase, 3·1 + 1 = 4. We can output 1.
In the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.
题意:给你一个数n,然后找出另一个数m使得n*m+1不是素数,将m输出来即可。
分析:直接从1开始遍历直到找到一个符合题意的即可
代码:
#include<iostream> #include<string> #include<cstdio> #include<cstring> #include<vector> #include<math.h> #include<map> #include<queue> #include<algorithm> using namespace std; const int inf = 0x3f3f3f3f; int n; int judge (int m){ int t=m*n+1; for (int i=2;i*i<=t;i++){ if (t%i==0)return 1;//不是素数,返回1 } return 0;//是素数,返回0 } int main () { while (cin>>n){ int m=1; while (1){ if (judge(m))break;//找到一个不是素数的m值 else m++; } cout<<m<<endl; } return 0; }
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