a01sa01to's competitive programming library.
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;
#include "../../../cpp/library/math/miller-rabin.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int q;
cin >> q;
while (q--) {
ull n;
cin >> n;
cout << (asalib::math::miller_rabin_test(n) ? "Yes" : "No") << '\n';
}
return 0;
}
#line 1 "tests/math/miller-rabin/libchecker.test.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;
#line 2 "library/math/miller-rabin.hpp"
#line 4 "library/math/miller-rabin.hpp"
#include <concepts>
#line 6 "library/math/miller-rabin.hpp"
using namespace std;
namespace asalib {
namespace math {
template<integral T>
constexpr bool miller_rabin_test(T n) {
if (n < 2) [[unlikely]]
return false;
if (n % 2 == 0) return n == 2;
T d = n - 1, s = 0;
while (d % 2 == 0) d >>= 1, ++s;
assert(d % 2 == 1);
static_assert(sizeof(T) == 4 || sizeof(T) == 8, "T must be 32-bit or 64-bit integer type");
constexpr bool is_64bit = sizeof(T) == 8;
function<T(T, T, T)> modpow = [&](T a, T n, T mod) {
T res = 1;
while (n) {
if constexpr (is_64bit) {
if (n & 1) res = (__uint128_t) res * a % mod;
a = (__uint128_t) a * a % mod;
}
else {
if (n & 1) res = (unsigned long long) res * a % mod;
a = (unsigned long long) a * a % mod;
}
n >>= 1;
}
return res;
};
function<bool(T)> test = [&](T a) {
T x = modpow(a, d, n);
if (x == 0) [[unlikely]]
return false;
if (x == 1) [[unlikely]]
return true;
for (T _ = 0; _ < s; ++_) {
T y;
if constexpr (is_64bit)
y = (__uint128_t) x * x % n;
else
y = (unsigned long long) x * x % n;
if (y == 1 && x != 1 && x != n - 1) return false;
x = y;
}
return x == 1;
};
function<bool(vector<T>)> tests = [&](vector<T> basis) {
for (T a : basis)
if (!test(a)) return false;
return true;
};
if (n < 2'047) return test(2);
if (n < 1'373'653) return tests({ 2, 3 });
if (n < 9'080'191) return tests({ 31, 73 });
if (n < 25'326'001) return tests({ 2, 3, 5 });
if (n < 3'215'031'751) return tests({ 2, 3, 5, 7 });
if (n < 4'759'123'141) return tests({ 2, 7, 61 });
if (n < 1'122'004'669'633) return tests({ 2, 13, 23, 1662803 });
if (n < 2'152'302'898'747) return tests({ 2, 3, 5, 7, 11 });
if (n < 3'474'749'660'383) return tests({ 2, 3, 5, 7, 11, 13 });
if (n < 341'550'071'728'321) return tests({ 2, 3, 5, 7, 11, 13, 17 });
if (n < 3'825'123'056'546'413'051) return tests({ 2, 3, 5, 7, 11, 13, 17, 19, 23 });
if (ull(n) <= 18'446'744'073'709'551'615ULL) return tests({ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 });
// 18'446'744'073'709'551'616 は 2^64 であり、これ以上の数は 64 ビット整数型では表現できない
// TODO: 多倍長整数を使う場合は if を追加する
// TODO: C++23 以降なら __builtin_unreachable() -> std::unreachable() に変更可能
__builtin_unreachable();
}
} // namespace math
} // namespace asalib
#line 8 "tests/math/miller-rabin/libchecker.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int q;
cin >> q;
while (q--) {
ull n;
cin >> n;
cout << (asalib::math::miller_rabin_test(n) ? "Yes" : "No") << '\n';
}
return 0;
}