#include #include #include #include #include template using V = std::vector; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; using f32 = float; using f64 = double; using f80 = long double; template T bin_gcd(T a, T b) { if (!a || !b) return a | b; T shift = CTZ(a | b); a >>= CTZ(a); do { b >>= CTZ(b); if (a > b) { T t = a; a = b; b = t; } b -= a; } while (b); return a << shift; } template struct Montgomery_t { Unsigned x; static Unsigned mod; static Unsigned r2; static Unsigned inv; static constexpr int unsigned_bits = sizeof(Unsigned) * 8; static Unsigned modulus() { return mod; } static Unsigned reduce(DoubleUnsigned x) { Unsigned y = Unsigned(x >> unsigned_bits) - Unsigned((DoubleUnsigned(Unsigned(x) * inv) * mod) >> unsigned_bits); return Signed(y) < 0 ? y + mod : y; } static Unsigned to_montgomery(Unsigned w) { return reduce(DoubleUnsigned(w) * r2); } static Unsigned mul_inv(Unsigned n) { Unsigned u = 1, v = 0, x = 1ul << (unsigned_bits - 1); for (int i = 0; i < unsigned_bits; i++) { if (u & 1) u = (u + mod) >> 1, v = (v >> 1) + x; else u >>= 1, v >>= 1; } return -v; } static void set_mod(Unsigned m) { mod = m; inv = mul_inv(mod); r2 = -DoubleUnsigned(mod) % mod; } Montgomery_t(): x(0) { } Montgomery_t(Unsigned _x): x(to_montgomery(_x)) { } bool operator==(const Montgomery_t& rhs) const { return x == rhs.x; } bool operator!=(const Montgomery_t& rhs) const { return x != rhs.x; } Montgomery_t& operator+=(const Montgomery_t& rhs) { x += rhs.x - mod; if (Signed(x) < 0) x += mod; return *this; } Montgomery_t& operator-=(const Montgomery_t& rhs) { if (Signed(x -= rhs.x) < 0) x += 2 * mod; return *this; } Montgomery_t& operator*=(const Montgomery_t& rhs) { x = reduce(DoubleUnsigned(x) * rhs.x); return *this; } Montgomery_t operator+(const Montgomery_t &rhs) const { return Montgomery_t(*this) += rhs; } Montgomery_t operator-(const Montgomery_t &rhs) const { return Montgomery_t(*this) -= rhs; } Montgomery_t operator*(const Montgomery_t &rhs) const { return Montgomery_t(*this) *= rhs; } Montgomery_t operator-() const { return Montgomery_t() - Montgomery_t(*this); } Montgomery_t pow(u64 e) const { Montgomery_t ret{1}; for (Montgomery_t base = *this; e; e >>= 1, base *= base) if (e & 1) ret *= base; return ret; } Montgomery_t inverse() const { return pow(mod - 2); } Montgomery_t& operator/=(const Montgomery_t& rhs) { *this *= rhs.inverse(); return *this; } Montgomery_t operator/(const Montgomery_t &rhs) const { return Montgomery_t(*this) /= rhs; } Unsigned from_montgomery() const { return reduce(x); } }; using m32 = Montgomery_t; template<> u32 m32::mod = 0; template<> u32 m32::inv = 0; template<> u32 m32::r2 = 0; using m64 = Montgomery_t; template<> u64 m64::mod = 0; template<> u64 m64::inv = 0; template<> u64 m64::r2 = 0; template bool miller_rabin(Unsigned N, const V& bases) { mint::set_mod(N); Unsigned M = N - 1; int s = __builtin_ctzll(N - 1); Unsigned d = (N - 1) >> s; mint one{1}, rev{N - 1}; for (const auto& base : bases) { if (N <= base) break; u64 t = d; mint y = mint(base).pow(t); while (t != M && y != one && y != rev) { y *= y; t <<= 1; } if (y != rev && (!(t & 1))) return false; } return true; } bool is_prime(u64 N) { if (N <= 3ul) return N == 2ul || N == 3ul; if (!(N & 1)) return false; if (N < (1u << 31)) return miller_rabin(u32(N), {2u, 7u, 61u}); return miller_rabin(N, {2u, 325u, 9375u, 28178u, 450775u, 9780504u, 1795265022u}); } void Solve(void) { int T; scanf("%d", &T); while (T--) { u64 N; scanf("%llu", &N); printf("%llu %d\n", N, is_prime(N)); } } int main(void) { Solve(); return 0; }