#include using namespace std; namespace modint { class dynamic_modint { using mint = dynamic_modint; using i64 = __int64_t; using u64 = __uint64_t; using u128 = __uint128_t; using i128 = __int128_t; static u128 mod; static u128 r; static u128 n2; private: 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 < ((u128)1 << 64)); assert(m & 1); mod = m; n2 = -u128(m) % m; r = get_r(); } private: u64 a; public: dynamic_modint() : a(0) {} dynamic_modint(const i64& b) : a(reduce((u128(b) + 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); } 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; } friend mint operator/(const mint&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 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 u64& lhs, const mint& rhs) { return mint(lhs) / rhs; } friend mint operator/(const mint& lhs, const u64& rhs) { return lhs / mint(rhs); } 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); } mint pow(u128 e) const { mint pw(1), base(*this); while (e) { if (e & 1) { pw *= base; } base *= base; e >>= 1; } return pw; } friend ostream& operator<<(ostream& os, const mint& b) { return os << b.val(); } friend istream& operator>>(istream& is, mint& b) { int64_t t; is >> t; b = dynamic_modint(t); return (is); } mint inv() const { return pow(mod - 2); } u64 val() const { u64 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static u64 get_mod() { return mod; } }; typename dynamic_modint::u128 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'; } }