C :

#include <stdio.h>

///int integer[15] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};
int flag[15];
int result[15];
int stack[15],top = 0;
int N;
int haveResult;

int isprime(int n){
    for(int i = 2; i <= n / 2; i++){
        if(n % i == 0)
            return 0;
    }
    return 1;
}

void print(){
    int i;
    for(i = 0; i < N - 1; i++){
        printf("%d ",result[i]);
    }
    printf("%d\n",result[i]);
}

void primeCircle(int cur){///cur将要填写的位置

    if(cur == N){
        print();
        haveResult = 1;
        return ;
    }

    for(int i = 2; i <= N; i++){///遍历每一个可填数字
        if(flag[i - 1] == 0 && isprime(result[cur - 1] + i)){
            ///最后一个数字与第一个数字1的和不是质数
            if(cur == N - 1 && !isprime(i + 1)){
                break;
            }
            result[cur] = i;
            flag[i - 1] = 1;
            primeCircle(cur + 1);
            ///返回上一层时，当前位置设置为未入选
            if(flag[result[cur] - 1] == 1){
                flag[result[cur] - 1] = 0;
            }
        }
    }
}

int main(void){
    result[0] = 1;
    flag[0] = 1;
    stack[top++] = 1;

    while(scanf("%d",&N) != EOF){
        haveResult = 0;
        primeCircle(1);
        if(haveResult == 0)
            printf("No Solution\n");
    }

    return 0;
}

C++ :

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
int n,a[51]={0},b[51],ans=0;
bool f;
bool pd1()
{
     memset(b,0,sizeof(b));
     for(int i=1;i<=n;i++)
       if(b[a[i]]==1)return false;
       else b[a[i]]++;
     return true;
}
bool ok(int x)
{
     for(int i=2;i<=sqrt(x);i++)
       if(x%i==0)return true;
     return false;
}
bool pd2()
{
     for(int i=1;i<=n-1;i++)
       if(ok(a[i]+a[i+1]))
         return false;
     if(ok(a[n]+a[1]))return false;
     return true;
}
void find(int m)
{
     if(m==n+1)
     {
       if(pd1()&&pd2()&&a[1]==1)
       {
         for(int i=1;i<=n-1;i++)
           cout<<a[i]<<" ";
         cout<<a[n]<<endl;
         ans++;
       }
       return;
     }
     for(int i=1;i<=n;i++)
     {
       a[m]=i;
       find(m+1);
     }
}
int main()
{
    cin>>n;a[1]=1;
    find(1);
    if(ans==0)cout<<"No Solution"<<endl;
    return 0;
}

Java :

import java.util.Scanner;

public class Main {
	static int N;
	static int visited[];
	static int arr[];
	static int count=0;
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner input=new Scanner(System.in);
		N=input.nextInt();
		visited=new int[N+1];
		arr=new int[N+1];
		for(int i=1;i<=N;i++) {
			arr[i]=i;
		}
		visited[1]=1;

		dfs(2);
		if(count==0) {
			System.out.println("No Solution");
		}
	}
	
	static void dfs(int n) {
		if(n==N+1) {
			if(sushu(arr[N]+1)) {
				for(int i=1;i<=N;i++) {
					System.out.print(arr[i]+" ");
				}
				count++;
				System.out.println();
			}
			return ;
		}else {
			for(int i=2;i<=N;i++) {
				if(visited[i]==0) {
					if(arr[n-1] %2==0 &&i %2 !=0) {
						if(sushu(arr[n-1]+i)) {
							arr[n]=i;
							visited[i]=1;
							dfs(n+1);
							visited[i]=0;
							visited[i]=0;
						}

					}
					if(arr[n-1] %2!=0 && i %2 ==0) {
						if(sushu(arr[n-1]+i)) {
							arr[n]=i;
							visited[i]=1;
							dfs(n+1);
							visited[i]=0;
							visited[i]=0;
						}
					}
				}
			}
		}
	}
	
	static boolean sushu(int n) {
		for(int i=2;i<n;i++) {
			if(n%i==0) {
				return false;
			}
		}
		return true;
	}

}