Here is my code, what can make my code run faster? Please check it up...

#include <iostream>
#include <cmath>
using namespace std;
bool prime(long long x)
{
    int i;

    if(x==2)
       return true;
    else if(x%2==0)
       return false;

    for(i=3; i*i<=x; i+=2)
        if(x%i==0)
           return false;
    return true;

}
int main()
{
    long long K, s;

    cin>>K;
    if(prime(K)==true)
    {
        cout<<K-1;
        return 0;
    }
    else
    {
        for(long long i=3; i<499999950; i++)
        {
            if(K%i==0)
            {
                cout<<i-1;
                return 0;
            }
        }
    }
    return 0;
}

Функция Prime может быть встроена в main

Вместо
if(Prime(K)==true)
можно писать
if(Prime(K))

oh my... =)

This lazy code gets AC in 0.562s
#include <cstdio>
int n,r;
int main()
{
.scanf("%d", &n);
.r=2;
.while ( n % (r+1) != 0 )
..++r;
.printf("%d",r);
.return 0;
}

And this a little bit (only a little) improved, especially for you, gets AC in 0.296s.
#include <cstdio>
int n,r;
int main()
{
.scanf("%d", &n);
.if ( n % 3 == 0 )
.printf("2");
.else if ( n % 4 == 0 )
..printf("3");
.else
.{
..r=4;
..while ( n % ++r != 0 )
...++r;
..printf("%d",r-1);
.}
.return 0;
}