#include<iostream> #include<string> #include<iomanip> #include<cmath> #include<vector> #include<algorithm> #include<ctime> #include <random> #include <limits> using namespace std; #define int long long #define endl "\n" long long power(long long x, long long n, long long mod){ long long ans = 1; while(n){ if(n&1) ans *= x; n >>= 1; x *= x; x %= mod; ans %= mod; } return ans; } bool Miller_Rabin(long long num, long long k){ if(num <= 1) return false; else if(num == 2) return true; else if(num%2 == 0) return false; long long s = 0, d = 0; random_device rnd; mt19937 mt(rnd()); // uniform_int_distribution<> rd(1,min((int)numeric_limits<int>::max(), num-1)); for(long long n = num-1;;){ if(n%2){ d = n; break; } else s++, n >>= 1; } for(long long i = 0; i < k; i++){ // long long a = rd(mt), n = d, a2 = 1; long long a = mt()%(num-1)+1, n = d, a2 = 1; bool flag = true; a2 = power(a, d, num); if(a2 == 1) continue; for(long long r = 0, two = 1; r < s; r++, two <<= 1){ a2 = power(a, two*d, num); if(a2 == num-1){ flag = false; break; } } if(flag) return false; } return true; } signed main(){ // cin.tie(0); // ios::sync_with_stdio(false); // cout<<fixed<<setprecision(10); int n; cin>>n; for(int i = 0; i < n; i++){ int x; cin>>x; cout<<x<<" "<<Miller_Rabin(x, 1000)<<endl; } return 0; }