#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#include "../../cpp/template/template.cpp"
#include "../../cpp/math/miller-rabin.cpp"
int main(){
int q;cin>>q;
for(int i = 0; q > i; i++){
long long n;cin>>n;
cout << (MillerRabinCheck(n) ? "Yes" : "No") << endl;
}
}
#line 1 "cpp/z_test/yosupo-primality_test.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#line 2 "cpp/template/template.cpp"
//yukicoder@cpp17
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <random>
#include <bitset>
#include <complex>
#include <utility>
#include <numeric>
#include <functional>
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);
P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};
template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/
/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
cin.tie(0);
ios::sync_with_stdio(false);
}
*/
#line 4 "cpp/z_test/yosupo-primality_test.test.cpp"
#line 2 "cpp/math/binary-power-method.cpp"
template <typename T>
T uPow(T z,T n, T mod){
T ans = 1;
while(n != 0){
if(n%2){
ans*=z;
if(mod)ans%=mod;
}
n >>= 1;
z*=z;
if(mod)z%=mod;
}
return ans;
}
#line 2 "cpp/math/miller-rabin.cpp"
/*
true: 素数
false: 合成数
*/
template<typename T>
bool MillerRabinCheck(T n){
if(n == 1)return false;
if(n%2 == 0){
return n == 2;
}
__int128 d = n-1;
__int128 s = 0;
while(d%2 == 0){
d/=2;
s++;
}
vector<__int128> base = {2,3,5,7,11,13,17,19,23,29,31,37};
for(int i = 0; base.size() > i; i++){
if(base[i] >= n)break;
long long current = (long long)uPow(base[i],d,(__int128)n);
if(current == 1 || current == n-1)continue;
bool ok = false;
for(int j = 0; s > j; j++){
current = ((__int128)current * (__int128)current) % n;
if(current == n-1){
ok = true;
break;
}
}
if(!ok)return false;
}
return true;
}
#line 6 "cpp/z_test/yosupo-primality_test.test.cpp"
int main(){
int q;cin>>q;
for(int i = 0; q > i; i++){
long long n;cin>>n;
cout << (MillerRabinCheck(n) ? "Yes" : "No") << endl;
}
}
cpp/z_test/yosupo-primality_test.test.cpp
cpp/geometry/two-points-distance.cpp