#pragma once #include using namespace std; namespace modint { class dynamic_modint { using i64 = int64_t; using u64 = uint64_t; using u128 = __uint128_t; using i128 = __int128_t; using mint = modint::dynamic_modint; static u64 mod; static u64 R; static u64 n2; static u64 get_r() { u64 ret = mod; for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret; return ret; } public: static void set_mod(u64 m) { assert(m < (1LL << 62)); assert((m & 1) == 1); mod = m; n2 = -u128(m) % m; R = get_r(); assert(R * mod == 1); } static u64 get_mod() { return mod; } protected: u128 a; public: dynamic_modint(const i64& v = 0) :a(reduce((u128)v + mod)* n2) {} private: static u64 reduce(const u128& b) { return (b + u128(u64(b) * u64(-R)) * mod) >> 64; } public: mint& operator+=(const mint& b) { if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint& operator-=(const mint& b) { if (i64(a -= b.a) < 0) a += 2 * mod; return *this; } mint& operator*=(const mint& b) { a = reduce(u128(a) * b.a); return (*this); } mint& operator/=(const mint& b) { *this *= b.inv(); return *this; } mint operator+(const mint& b) const { return mint(*this) += b; } mint operator-(const mint& b) const { return mint(*this) -= b; } mint operator*(const mint& b) const { return mint(*this) *= b; } mint operator/(const mint& b) const { return mint(*this) /= b; } bool operator==(const mint& b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(const mint& b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } mint operator-() const { return mint() - mint(*this); } u64 val() { assert(mod); u128 v = reduce(a); if (v >= mod) { v -= mod; } return v; } mint pow(u128 e) const { mint pw(1), base((*this)); while (e) { if (e & 1) { pw *= base; } base *= base; e >>= 1; } return pw; } mint inv() const { return pow(mod - 2); } }; typename dynamic_modint::u64 dynamic_modint::mod, dynamic_modint::R, dynamic_modint::n2; }; using modint::dynamic_modint; #pragma once //#include"math/mod_pow.hpp" namespace prime { namespace miller { using i128 = __int128_t; using u128 = __uint128_t; using u64 = __uint64_t; using mint = modint::dynamic_modint; bool miller_rabin(u64 n, const u64 bases[], int siz) { if (mint::get_mod() != n) { mint::set_mod(n); } u64 d = n - 1; u64 q = __builtin_ctz(d); d >>= q; for (int i = 0; i < siz; i++) { u64 a = bases[i]; if (a == n) { return true; } else if (n % a == 0) { return false; } if (mint(a).pow(d).val() != 1) { bool flag = true; for (u64 r = 0; r < q; r++) { mint pow = mint(a).pow(d * (1ll << r)); if (pow.val() == n - 1) { flag = false; break; } } if (flag) { return false; } } } return true; } bool is_prime(u64 n) { static constexpr u64 bases_int[3] = { 2, 7, 61 }; // intだと、2,7,61で十分 static constexpr u64 bases_ll[7] = { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }; if (n < 2) { return false; } else if (n == 2) { return true; } else if (~n & 1) { return false; } if (n < (1ul << 31)) { return miller_rabin(n, bases_int, 3); } else { return miller_rabin(n, bases_ll, 7); } } }; }; using prime::miller::is_prime; ///@brief fast prime check(MillerRabinの素数判定) int main() { int n; cin >> n; while (n--) { long long x; cin >> x; cout << x << ' ' << is_prime(x) << '\n'; } }