396B


  Posted on 19 Dec 2014
number theory

Solution


#include <cstdio>
using namespace std;

#define LL long long

int n;

LL gcd(LL a,LL b){
    if (a==0) return 1;
    if (a<0) return gcd(-a,b);
    while (b){
	LL t=a%b; a=b; b=t;
    }
    return a;
}

bool is_prime(int a)
{
	for (int i = 2; i * i <= a; i++)
	{
		if (a % i == 0)
			return false;
	}
	return true;
}

int main()
{
	//input
	int t;
	scanf("%d", &t);
	while (t--)
	{
		scanf("%d", &n);
		if (n == 2)
		{
			puts("1/6");
			continue;
		}
		int left = n;
		while (!is_prime(left))
			left--;
		int right = n + 1;
		while (!is_prime(right))
			right++;
		LL up = 1LL * (left - 2) * right + 2LL * (n - left + 1);
		LL down = 2LL * left * right;
		LL g = gcd(up, down);
		up /= g;
		down /= g;
		printf("%lld/%lld\n", up, down);
	}
	return 0;
}