A. PolandBall and Hypothesis
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
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.
#include<bits/stdc++.h>
using namespace std;
#define N 1000000
int f[N];
int isprime(int n){
int i;
int ok=0;
for(i=2;i*i<=n;i++){
if(n%i==0){
ok=1;
break;
}
}
if(ok)
return 0;
else
return 1;
}
int top=0;
int filter(int bound){
for(int i=1;i<=bound;i++){
if(isprime(i))
f[top++]=i;
}
}
int check(int key){
int r=upper_bound(f,f+top,key)-lower_bound(f,f+top,key);
if(r==1)
return 1;
else
return 0;
}
int main(){
filter(1000000+5);
int n;
cin>>n;
for(int i=1;;i++){
int m=i*n+1;
if(!check(m)){
cout<<i<<endl;
break;
}
}
return 0;
}