#pragma region opt #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma endregion opt #include #pragma region type using i8 = std::int8_t; using i16 = std::int16_t; using i32 = std::int32_t; using i64 = std::int64_t; using u8 = std::uint8_t; using u16 = std::uint16_t; using u32 = std::uint32_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 using vec = std::vector; template using vvec = std::vector>; template using vvvec = std::vector>>; template using pvec = std::pair, std::vector>; #pragma endregion type #pragma region MACRO for #define FOR(i,a,b) for(int i=(a), i##_len=(b); i((obj).size())) #pragma endregion MACRO container #pragma region MACRO bits #define POPCNT32(a) __builtin_popcount((a)) #define POPCNT64(a) __builtin_popcountll((a)) #define CTZ32(a) __builtin_ctz((a)) #define CLZ32(a) __builtin_clz((a)) #define CTZ64(a) __builtin_ctzll((a)) #define CLZ64(a) __builtin_clzll((a)) #define HAS_SINGLE_BIT32(a) (__builtin_popcount((a)) == (1)) #define HAS_SINGLE_BIT64(a) (__builtin_popcountll((a)) == (1)) #define MSB32(a) ((31) - __builtin_clz((a))) #define MSB64(a) ((63) - __builtin_clzll((a))) #define BIT_WIDTH32(a) ((a) ? ((32) - __builtin_clz((a))) : (0)) #define BIT_WIDTH64(a) ((a) ? ((64) - __builtin_clzll((a))) : (0)) #define LSBit(a) ((a) & (-(a))) #define CLSBit(a) ((a) & ((a) - (1))) #define BIT_CEIL32(a) ((!(a)) ? (1) : ((POPCNT32(a)) == (1) ? ((1u) << ((31) - CLZ32((a)))) : ((1u) << ((32) - CLZ32(a))))) #define BIT_CEIL64(a) ((!(a)) ? (1) : ((POPCNT64(a)) == (1) ? ((1ull) << ((63) - CLZ64((a)))) : ((1ull) << ((64) - CLZ64(a))))) #define BIT_FLOOR32(a) ((!(a)) ? (0) : ((1u) << ((31) - CLZ32((a))))) #define BIT_FLOOR64(a) ((!(a)) ? (0) : ((1ull) << ((63) - CLZ64((a))))) #define _ROTL32(x, s) (((x) << ((s) % (32))) | (((x) >> ((32) - ((s) % (32)))))) #define _ROTR32(x, s) (((x) >> ((s) % (32))) | (((x) << ((32) - ((s) % (32)))))) #define ROTL32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTR32((x), -(s))) : (_ROTL32((x), (s))))) #define ROTR32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTL32((x), -(s))) : (_ROTR32((x), (s))))) #define _ROTL64(x, s) (((x) << ((s) % (64))) | (((x) >> ((64) - ((s) % (64)))))) #define _ROTR64(x, s) (((x) >> ((s) % (64))) | (((x) << ((64) - ((s) % (64)))))) #define ROTL64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTR64((x), -(s))) : (_ROTL64((x), (s))))) #define ROTR64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTL64((x), -(s))) : (_ROTR64((x), (s))))) #pragma endregion MACRO bits #pragma region util template inline bool chmax(T& a,T b){ if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a,T b){ if (a > b) { a = b; return 1; } return 0; } #pragma endregion util #pragma region IO // -2147483648 ~ 2147483647 (> 10 ^ 9) i32 in_i32(void) { i32 c, x = 0, f = 1; while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f; while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return f * x; } static inline void out_i32_inner(i32 x) { if (x >= 10) out_i32_inner(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void out_i32(i32 x) { if (x < 0) { putchar_unlocked('-'); x = -x; } out_i32_inner(x); } // -9223372036854775808 ~ 9223372036854775807 (> 10 ^ 18) i64 in_i64(void) { i64 c, x = 0, f = 1; while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f; while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return f * x; } static inline void out_i64_inner(i64 x) { if (x >= 10) out_i64_inner(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void out_i64(i64 x) { if (x < 0) { putchar_unlocked('-'); x = -x; } out_i64_inner(x); } // 0 ~ 4294967295 (> 10 ^ 9) u32 in_u32(void) { u32 c, x = 0; while (c = getchar_unlocked(), c < 48 || c > 57); while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return x; } void out_u32(u32 x) { if (x >= 10) out_u32(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } // 0 ~ 18446744073709551615 (> 10 ^ 19) u64 in_u64(void) { u64 c, x = 0; while (c = getchar_unlocked(), c < 48 || c > 57); while (47 < c && c < 58) { x = x * 10 + c - 48; c = getchar_unlocked(); } return x; } void out_u64(u64 x) { if (x >= 10) out_u64(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void NL(void) { putchar_unlocked('\n'); } void SP(void) { putchar_unlocked(' '); } #pragma endregion IO u32 is_prime32(u32 n) { using m32 = u32; const m32 one = (u32)-1u % n + 1; const m32 r2 = (u64)(i64)-1 % n + 1; m32 N_ = n; for (int _ = 0; _ < 4; ++_) N_ *= 2 - N_ * n; const m32 N = N_; auto reduce = [](u64 a, m32 x, u32 mod) { u32 y = (u32)(a >> 32) - (u32)(((u64)((u32)a * x) * mod) >> 32); return (i32)y < 0 ? y + mod : y; }; auto to = [&reduce](u32 a, m32 x, m32 y, u32 mod) -> m32 { return reduce((u64)a * x, y, mod); }; auto mul = [&reduce](m32 x, m32 y, m32 z, u32 mod) -> m32 { return reduce(u64(x) * y, z, mod); }; auto pow = [&mul](m32 a, u32 k, m32 x, m32 z, u32 mod) -> m32 { m32 ret = x; m32 A = a; while (k > 0) { if (k & 1) ret = mul(ret, A, z, mod); A = mul(A, A, z, mod); k >>= 1; } return ret; }; u32 m = n - 1; m32 rev = to(m, r2, N, n); u32 d = m >> CTZ32(m); u32 base[] = { 2u, 7u, 61u }; for (int i = 0; i < 3; i++) { if (n <= base[i]) break; u32 t = d; m32 y = pow(to(base[i], r2, N, n), t, one, N, n); while (t != m && y != one && y != rev) { y = mul(y, y, N, n); t <<= 1; } if (y != rev && (!(t & 1))) return false; } return true; } u64 is_prime64(u64 n) { using m64 = u64; const m64 one = (u64)-1ull % n + 1; const m64 r2 = (u128)(i128)-1 % n + 1; m64 N_ = n; for (int _ = 0; _ < 5; _++) N_ *= 2 - N_ * n; const m64 N = N_; auto reduce = [](u128 a, m64 x, u64 mod) { u64 y = (u64)(a >> 64) - (u64)(((u128)((u64)a * x) * mod) >> 64); return (i64)y < 0 ? y + mod : y; }; auto to = [&reduce](u64 a, m64 x, m64 y, u64 mod) -> m64 { return reduce((u128)a * x, y, mod); }; auto mul = [&reduce](m64 x, m64 y, m64 z, u64 mod) -> m64 { return reduce(u128(x) * y, z, mod); }; auto pow = [&mul](m64 a, u64 k, m64 x, m64 z, u64 mod) -> m64 { m64 ret = x; m64 A = a; while (k > 0) { if (k & 1) ret = mul(ret, A, z, mod); A = mul(A, A, z, mod); k >>= 1; } return ret; }; u64 m = n - 1; m64 rev = to(m, r2, N, n); u64 d = m >> CTZ64(m); u64 base[] = { 2ul, 325ul, 9375ul, 28178ul, 450775ul, 9780504ul, 1795265022ul }; for (int i = 0; i < 7; i++) { if (n <= base[i]) break; u64 t = d; m64 y = pow(to(base[i], r2, N, n), t, one, N, n); while (t != m && y != one && y != rev) { y = mul(y, y, N, n); t <<= 1; } if (y != rev && (!(t & 1))) return false; } return true; } u32 is_prime(u64 n) { if (n <= 1) return 0; if (n <= 3) return 1; if (!(n & 1)) return 0; if (n < (1ull << 30)) return is_prime32(u32(n)); return is_prime64(n); } void Main() { // your source here i32 Q = in_i32(); while (Q--) { u64 x = in_u64(); out_u64(x); SP(); out_i32(is_prime(x)); NL(); } return; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr); std::cout << std::fixed << std::setprecision(13); std::cerr << std::fixed << std::setprecision(3); Main(); }