#pragma region opt #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma endregion opt #pragma region header #define _GNU_SOURCE #include #include #include #include #include #include #include #include #include #pragma endregion header #pragma region type /* signed integer */ typedef int8_t i8; typedef int16_t i16; typedef int32_t i32; typedef int64_t i64; typedef __int128_t i128; /* unsigned integer */ typedef uint8_t u8; typedef uint16_t u16; typedef uint32_t u32; typedef uint64_t u64; typedef __uint128_t u128; /* floating point number */ typedef float f32; typedef double f64; typedef long double f80; #pragma endregion type #pragma region macro #define MIN(a, b) (((a) < (b)) ? (a) : (b)) #define MAX(a, b) (((a) > (b)) ? (a) : (b)) #define SWAP(a, b) (((a) ^= (b)), ((b) ^= (a)), ((a) ^= (b))) #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 #pragma region io int read_int(void) { // -2147483648 ~ 2147483647 (> 10 ^ 9) int 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; } i32 in_i32(void) { // -2147483648 ~ 2147483647 (> 10 ^ 9) 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; } u32 in_u32(void) { // 0 ~ 4294967295 (> 10 ^ 9) 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; } i64 in_i64(void) { // -9223372036854775808 ~ 9223372036854775807 (> 10 ^ 18) 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; } u64 in_u64(void) { // 0 ~ 18446744073709551615 (> 10 ^ 19) 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; } static inline void write_int_inner(int x) { if (x >= 10) write_int_inner(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } void write_int(int x) { if (x < 0) { putchar_unlocked('-'); x = -x; } write_int_inner(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); } void out_u32(u32 x) { if (x >= 10) out_u32(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); } 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); } 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(' '); } void write_int_array(int *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); write_int(a[i]); } NL(); } void out_i32_array(i32 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_i32(a[i]); } NL(); } void out_u32_array(u32 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_u32(a[i]); } NL(); } void out_i64_array(i64 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_i64(a[i]); } NL(); } void out_u64_array(u64 *a, int a_len) { for (int i = 0; i < a_len; i++) { if (i) SP(); out_u64(a[i]); } NL(); } #pragma endregion io #pragma region xorshift const f64 _R_ = 1.0 / 0xffffffffffffffff; static u64 _xorshift_state_ = 88172645463325252ULL; u64 next_rand_xorshift(void) { _xorshift_state_ = _xorshift_state_ ^ (_xorshift_state_ << 7); return _xorshift_state_ = _xorshift_state_ ^ (_xorshift_state_ >> 9); } void rand_init_xorshift(u64 seed) { _xorshift_state_ += seed; (void)next_rand_xorshift(); } u64 random_range_xorshift(u64 l, u64 r) { return next_rand_xorshift() % (r - l + 1) + l; } f64 probability_xorshift(void) { return _R_ * next_rand_xorshift(); } #pragma endregion xorshift #pragma region binary gcd u64 bin_gcd(u64 a, u64 b) { if (!a || !b) return a | b; u64 s = __builtin_ctzll(a | b); u64 t; a >>= __builtin_ctzll(a); do { b >>= __builtin_ctzll(b); if (a > b) t = a, a = b, b = a; b -= a; } while (b); return a << s; } #pragma endregion binary gcd #pragma region jacobi symbol int jacobi_symbol(i64 a, u64 n){ u64 t; int j = 1; while(a) { if (a < 0) { a = -a; if ((n & 3) == 3) j = -j; } int s = __builtin_ctzll(a); a >>= s; if (((n & 7) == 3 || (n & 7) == 5) && (s & 1)) j = -j; if ((a & n & 3) == 3) j = -j; t = a, a = n, n = t; a %= n; if (a > n / 2) a -= n; } return n == 1 ? j : 0; } #pragma endregion jacobi symbol #pragma region solovay_strassen primality test u64 pow_mod(u64 base, u64 indx, u64 mod) { u64 ret = 1ull; base = (base >= mod) ? base % mod : base; while (indx) { if (indx & 1) ret = (u64)(((u128)ret * base) % mod); base = (u64)(((u128)base * base) % mod); indx >>= 1; } return ret; } bool is_prime(u64 n) { if (n <= 1) return false; if (n <= 3) return true; if (!(n & 1)) return false; for (int _k = 0; _k < 200; _k++) { u64 a = random_range_xorshift(2, n - 1); if (bin_gcd(a, n) > 1) return false; int x = jacobi_symbol(a, n); u64 y = (x == -1) ? n - 1 : (u64)x; if (y == 0 || y != pow_mod(a, (n - 1) / 2, n)) return false; } return true; } #pragma endregion solovay_strassen primality test void Main(void) { int T = read_int(); while (T--) { u64 x = in_u64(); out_u64(x); SP(); write_int(is_prime(x)); NL(); } } int main(void) { Main(); return 0; }