verify/yosupo-primality_test.test.cpp

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Last update: 2025-04-30 03:58:59+00:00
Problem: https://judge.yosupo.jp/problem/primality_test

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#include "template"

#include "prime"


int main() { IO();
    int T=1;
    // cin >> T;

    while (T--) solve();
}

void solve() {
    int q; cin >> q;
    while (q--) {
        ll n; cin >> n;
        YN(isprime(n));
    }
}

#line 1 "verify/yosupo-primality_test.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#line 2 "util/template.hpp"
#ifdef poe
#define debug(x) cerr<<#x<<": "<<x<<endl
#else
#define debug(x)
// #pragma GCC target("arch=skylake-avx512")
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#endif
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using pi=pair<int,int>;
using pll=pair<ll,ll>;
using str=string;
template<class T>using vec=vector<T>;
using vi=vec<int>;using vvi=vec<vi>;using vvvi=vec<vvi>;using vvvvi=vec<vvvi>;using vvvvvi=vec<vvvvi>;
using vll=vec<ll>;using vvll=vec<vll>;using vvvll=vec<vvll>;using vvvvll=vec<vvvll>;using vvvvvll=vec<vvvvll>;
using vpi=vec<pi>;using vvpi=vec<vpi>;using vvvpi=vec<vvpi>;using vvvvpi=vec<vvvpi>;using vvvvvpi=vec<vvvvpi>;
using vpll=vec<pll>;using vvpll=vec<vpll>;using vvvpll=vec<vvpll>;using vvvvpll=vec<vvvpll>;using vvvvvpll=vec<vvvvpll>;
template<class T>using pq=priority_queue<T,vector<T>>;
template<class T>using pqg=priority_queue<T,vector<T>,greater<T>>;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define per(i,n) for(int i=(int)(n)-1;0<=i;i--)
#define per1(i,n) for(int i=(int)(n);0<i;i--)
#define range(i,x) for(auto&i:x)
#define range2(i,j,x) for(auto&[i,j]:x)
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define Sort(x) sort((x).begin(),(x).end())
#define troS(x) sort((x).rbegin(),(x).rend())
#define Reverse(x) reverse((x).begin(),(x).end())
#define uniq(x) sort((x).begin(),(x).end());(x).erase(unique((x).begin(),(x).end()),(x).end())
#define nextp(x) next_permutation((x).begin(),(x).end())
#define nextc(x,k) next_combination((x).begin(),(x).end(),k)
#define bit(x,i) (((x)>>(i))&1)
#define pf push_front
#define pb push_back
#define df pop_front
#define db pop_back
#define fi first
#define se second
#define elif else if
#define Yes cout<<"Yes"<<'\n'
#define No cout<<"No"<<'\n'
#define YN(x) cout<<((x)?"Yes":"No")<<'\n'
#define O(x) cout<<(x)<<'\n'
#define ismid(a,b,c) ((a)<=(b)&&(b)<(c))
template<class S,class T>bool chmin(S&a,T b){if(a>b){a=b;return true;}return false;}
template<class S,class T>bool chmax(S&a,T b){if(a<b){a=b;return true;}return false;}
template<class T>bool next_combination(T l,T r,int k){T m=l+k;if(l==r||l==m||r==m)return false;T t=m;while(l!=t){t--;if(*t<*(r-1)){T d=m;while(*t>=*d)d++;iter_swap(t,d);rotate(t+1,d+1,r);rotate(m,m+(r-d)-1,r);return true;}}rotate(l,m,r);return false;}
template<class T>T Min(T a,T b){return a<b?a:b;}
template<class T,class...Args>T Min(T a,T b,Args...args){return Min(Min(a,b),args...);}
template<class T>T Max(T a,T b){return a>b?a:b;}
template<class T,class...Args>T Max(T a,T b,Args...args){return Max(Max(a,b),args...);}
template<class T>T Sum(T a){return a;}
template<class T,class... Args>T Sum(T a,Args... args){return a+Sum(args...);}
template<class T>T Max(const vector<T>&v){return *max_element(all(v));}
template<class T>T Min(const vector<T>&v){return *min_element(all(v));}
template<class T>T Sum(const vector<T>&v){return accumulate(all(v),T(0));}
template<class S,class T>T Max(const pair<S,T>&p){return max(p.first,p.second);}
template<class S,class T>T Min(const pair<S,T>&p){return min(p.first,p.second);}
template<class S,class T>T Sum(const pair<S,T>&p){return p.first+p.second;}
template<class S,class T>istream&operator>>(istream&s,pair<S,T>&p){s>>p.first>>p.second;return s;}
template<class S,class T>ostream&operator<<(ostream&s,pair<S,T>&p){s<<p.first<<' '<<p.second<<'\n';return s;}
template<class T>istream&operator>>(istream&s,vector<T>&v){for(auto&i:v)s>>i;return s;}
template<class T>ostream&operator<<(ostream&s,vector<T>&v){for(auto&i:v)s<<i<<' ';s<<'\n';return s;}
template<class F>long long bsearch(long long ok,long long ng,F&f){while(abs(ok-ng)>1){long long mid=(ok+ng)/2;if(f(mid))ok=mid;else ng=mid;}return ok;}
const int dxy[5]={0,1,0,-1,0};
const int dx[8]={0,1,0,-1,1,1,-1,-1};
const int dy[8]={1,0,-1,0,1,-1,1,-1};
#define nl '\n'
#define sp ' '
#define inf ((1<<30)-(1<<15))
#define INF (1LL<<61)
#define mod 998244353

void IO() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout<<fixed<<setprecision(30);
}

void solve();
#line 3 "math/prime.hpp"
using namespace std;
// 素数判定 O(log n)
bool isprime(long long n) {
    if (n <= 1) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    int flag = 1;
    if (n < 4759123141LL) flag = 0;
    vector<vector<long long>> tests = {{2, 7, 61}, {2, 325, 9375, 28178, 450775, 9780504, 1795265022}};
    long long s = 0, d = n - 1;
    while (d % 2 == 0) {
        ++s;
        d >>= 1;
    }
    for (auto a : tests[flag]) {
        if (n <= a) return true;
        __int128_t x = 1, a2=a%n, d2 = d;
        while (d2) {
            if (d2 & 1) x = x * a2 % n;
            a2 = a2 * a2 % n;
            d2 >>= 1;
        }
        if (x != 1) {
            long long t;
            for (t = 0; t < s; ++t) {
                if (x == n - 1) break;
                x = x * x % n;
            }
            if (t == s) return false;
        }
    }
    return true;
}
// n 以下の素数を列挙する O(n log log n)
vector<int> enumprimes(int n) {
    vector<bool> primeflag(n+1);
    vector<int> re;
    for (long long i=2; i<=n; i++) {
        if (primeflag[i]) continue;
        re.push_back(i);
        for (long long j=i*i; j<=n; j+=i) {
            primeflag[j] = true;
        }
    }
    return re;
}
// 素因数分解をする O(n^0.25)
void factorize(long long n, vector<long long>& factors) {
    if (n <= 1) return;
    if (isprime(n)) {
        factors.push_back(n);
        return;
    }
    if (n % 2 == 0) {
        while (n % 2 == 0) {
            factors.push_back(2);
            n /= 2;
        }
        factorize(n, factors);
        return;
    }
    while (true) {
        __int128_t x = rand() % (n - 2) + 2;
        __int128_t y = x;
        __int128_t c = rand() % (n - 1) + 1;
        __int128_t m = 1;
        while (m == 1) {
            x = (x * x + c) % n;
            y = (y * y + c) % n;
            y = (y * y + c) % n;
            m = gcd((long long)(x - y + n), n);
            if (m == n) break;
        }
        if (m != n) {
            factorize(m, factors);
            factorize(n / m, factors);
            return;
        }
    }
}
#line 4 "verify/yosupo-primality_test.test.cpp"

int main() { IO();
    int T=1;
    // cin >> T;

    while (T--) solve();
}

void solve() {
    int q; cin >> q;
    while (q--) {
        ll n; cin >> n;
        YN(isprime(n));
    }
}