#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 res = mod; for (int i = 0; i < 5; i++) { res *= 2 - mod * res; } return res; } static u64 reduce(const u128& v) { u128 m = u128(u64(v) * u64(-R)) * mod; u64 t = (v + m) >> 64; return t; } public: static void set_mod(u64 mod_) { assert(mod_ < ((u128)(1) << 64)); assert(mod_ & 1); mod = mod_; n2 = -(u128)(mod_) % mod_; 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) {} mint& operator=(const u64& v) { return (*this) = mint(v); } mint& operator+=(const mint& rhs) { if (i64(a += rhs.a - 2 * mod) < 0) { a += 2 * mod; } return (*this); } mint& operator-=(const mint& rhs) { if (i64(a -= rhs.a) < 0) { a += 2 * mod; } return (*this); } mint& operator*=(const mint& rhs) { a = reduce((u128)(a)*rhs.a); return (*this); } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } mint& operator+=(const u64& rhs) { return (*this) += mint(rhs); } mint& operator-=(const u64& rhs) { return (*this) -= mint(rhs); } mint& operator*=(const u64& rhs) { return (*this) *= mint(rhs); } friend mint operator+(const mint& lhs, const u64& rhs) { return mint(lhs) += rhs; } friend mint operator+(const u64& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const u64& rhs) { return mint(lhs) -= rhs; } friend mint operator-(const u64& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator*(const mint& lhs, const u64& rhs) { return mint(lhs) *= rhs; } friend mint operator*(const u64& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend bool operator==(mint& lhs, mint& rhs) { if (lhs.a >= mod) { lhs.a -= mod; } if (rhs.a >= mod) { rhs.a -= mod; } return lhs.a == rhs.a; } u64 val() { assert(mod); u64 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); } mint& operator/=(const mint& rhs) { return (*this) *= rhs.inv(); } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend mint operator/(const u64& lhs, const mint& rhs) { return mint(lhs) / rhs; } friend mint operator/(const mint& lhs, const u64& rhs) { return lhs / mint(rhs); } }; typename dynamic_modint::u64 dynamic_modint::mod, dynamic_modint::n2, dynamic_modint::R; }; 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'; } }