number_theory/test/primality_test.test.cpp

View this file on GitHub
Last update: 2025-06-28 10:05:47+09:00
Problem: https://judge.yosupo.jp/problem/primality_test

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#define FAST_IO
#include "../../number_theory/primality.hpp"
#include "../../template/template.hpp"

void solve() {
    I32(q);
    REP(qi, q) {
        U64(x);
        cout << (is_prime(x) ? "Yes\n" : "No\n");
    }
}

int main() {
    i32 t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
}

#line 1 "number_theory/test/primality_test.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#define FAST_IO
#line 2 "number_theory/primality.hpp"

namespace primality {

using u64 = unsigned long long;
using u128 = __uint128_t;

u64 inv_64(u64 n) {
    u64 r = n;
    for (int i = 0; i < 5; ++i) {
        r *= 2 - n * r;
    }
    return r;
}

// n: odd, < 2^{62}
struct Montgomery64 {
    u64 n, mni, p;
    Montgomery64(u64 n) : n(n), mni(-inv_64(n)), p(-1ULL % n + 1) {}
    u64 mulmr(u64 xr, u64 yr) const {
        u128 z = (u128)xr * yr;
        u64 ret = (z + (u128)((u64)z * mni) * n) >> 64;
        if (ret >= n) {
            ret -= n;
        }
        return ret;
    }
    u64 mr(u64 xr) const {
        u64 ret = (xr + (u128)(xr * mni) * n) >> 64;
        if (ret >= n) {
            ret -= n;
        }
        return ret;
    }
    u64 pow(u64 xr, u64 t) const {
        u64 ret = p;
        while (t) {
            if (t & 1) {
                ret = mulmr(ret, xr);
            }
            xr = mulmr(xr, xr);
            t >>= 1;
        }
        return ret;
    }
};

bool is_prime(u64 n) {
    if (n == 2) {
        return true;
    }
    if (n == 1 || n % 2 == 0) {
        return false;
    }
    u64 s = __builtin_ctzll(n - 1);
    u64 d = (n - 1) >> s;
    u64 base[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    Montgomery64 mont(n);
    u64 fl = n - mont.p;
    for (u64 b : base) {
        b = mont.mr(b);
        if (!b) {
            continue;
        }
        u64 t = mont.pow(b, d);
        if (t == mont.p) {
            continue;
        }
        u64 i = 0;
        for (; i < s; ++i) {
            if (t == fl) {
                break;
            }
            t = mont.mulmr(t, t);
        }
        if (i == s) {
            return false;
        }
    }
    return true;
}

}  // namespace primality

bool is_prime(unsigned long long n) {
    return primality::is_prime(n);
}
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define F64(...)     \
    f64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
#line 5 "number_theory/test/primality_test.test.cpp"

void solve() {
    I32(q);
    REP(qi, q) {
        U64(x);
        cout << (is_prime(x) ? "Yes\n" : "No\n");
    }
}

int main() {
    i32 t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
}