Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.
The conjecture has been shown to hold for all integers less than 4 × 1018
Bismillahir Rahmanir Rahim
///Author: Tanvir Ahmmad
///CSE,Islamic University,Bangladesh
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<string>
#include<cstring>
#include<sstream>
#include<cmath>
#include<cstring>
#include<vector>
#include<queue>
#include<map>
#include<set>
#include<stack>
#include<vector>
#include<iterator>
#include <functional> ///sort(arr,arr+n,greater<int>()) for decrement of array
/*every external angle sum=360 degree
angle find using polygon hand(n) ((n-2)*180)/n*/
///Floor[Log(b) N] + 1 = the number of digits when any number is represented in base b
using namespace std;
typedef long long ll;
bool prime(ll num)
{
for(ll i=2;i*i<=num;i++)
if(num%i==0) return false;
return true;
}
int main()
{
ll num;
cin>>num;
if(prime(num)==true) cout<<"1"<<endl;
else if(num%2==1)
{
if(prime(num-2)==false) cout<<"3"<<endl;
else cout<<"2"<<endl;
}
else cout<<"2"<<endl;
return 0;
}
///Alhamdulillah
Problem Link: https://codeforces.com/problemset/problem/735/D
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