#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#define MAX 650
#define INF 1000000000

int graph[MAX][MAX] , value[MAX];
bool NotPrime[2001000] ;
int prim(int n)
{
	int lowCost[MAX];
	bool visited[MAX] ;
	memset(visited,false,sizeof(visited)) ;
	int sum = 0 ;
	for(int i = 0 ; i < n ; ++i)
	{
		lowCost[i] = graph[0][i] ;
	}
	visited[0] = true ;
	for(int i = 0 ; i < n-1 ; ++i)
	{
		int index = -1 , min = INF ;
		for(int j = 0 ; j < n ; ++j)
		{
			if(!visited[j] && lowCost[j]<min)
			{
				index = j ;
				min = lowCost[j] ;
			}
		}
		if(index == -1)
		{
			if(i < n-1)
			{
				return INF ;
			}
			break ;
		} 
		sum += min ;
		visited[index] = true ;
		for(int j = 0 ; j < n ; ++j)
		{
			if(!visited[j] && lowCost[j] > graph[index][j])
			{
				lowCost[j] = graph[index][j] ;
			}
		}
	}
	return sum ;
}

int min(int a , int b)
{
	return a>b?b:a ;
}

int main()
{
	int t ;
	NotPrime[0] = NotPrime[1] = true ;
	for(int i = 2 ; i < 2001000/2 ; ++i)
	{
		for(int j = 2 ; j*i < 2001000 ; ++j)
		{
			NotPrime[j*i] = true ;
		}
	}
	scanf("%d",&t);
	while(t--)
	{
		int n ;
		scanf("%d",&n);
		for(int i = 0 ; i < n ; ++i)
		{
			scanf("%d",&value[i]) ;
		}
		for(int i = 0 ; i < n ; ++i)
		{
			for(int j = 0 ; j < i ; ++j)
			{
				if(!NotPrime[value[i]] || !NotPrime[value[j]] || !NotPrime[abs(value[i]+value[j])])
				{
					graph[i][j] = graph[j][i] = min(min(value[i],value[j]),abs(value[i]-value[j]))  ;
				}
				else
				{
					graph[i][j] = graph[j][i] = INF ;
				}
			}
			graph[i][i] = 0 ;
		}
		int sum = prim(n) ;
		if(sum == INF)
		{
			puts("-1");
		}
		else
		{
			printf("%d\n",sum) ;
		}
	}
	return 0 ;
}