#include #include #include #include #include #include #include typedef int8_t i8; typedef int16_t i16; typedef int32_t i32; typedef int64_t i64; typedef __int128_t i128; typedef uint8_t u8; typedef uint16_t u16; typedef uint32_t u32; typedef uint64_t u64; typedef __uint128_t u128; static inline u64 ctz(u64 n) { return __builtin_ctzll(n); } static inline u64 clz(u64 n) { return __builtin_clzll(n); } static inline u64 popcnt(u64 n) { return __builtin_popcountll(n); } static inline u64 gcd(u64 u, u64 v) { if (u == 0) return v; if (v == 0) return u; u64 k; for (k = 0; ((u | v) & 1) == 0; ++k) { u >>= 1; v >>= 1; } while ((u & 1) == 0) u >>= 1; do { while ((v & 1) == 0) v >>= 1; if (u > v) { u ^= v; v ^= u; u ^= v; } v = v - u; } while (v != 0); return u << k; } typedef struct Montgomery_t { u64 m, r, n2; u64 x; } m64; m64 make_montgomery(u64 mod) { m64 result; assert(mod != 0); assert(mod & 1 != 0); result.m = mod; result.n2 = -(u128)(mod) % mod; result.r = mod; for (int _ = 0; _ < 5; _++) result.r *= 2 - result.m * result.r; result.r = -result.r; return result; } u64 MR(m64 p, u128 b) { return (b + (u128)((u64)b * p.r) * p.m) >> 64; } u64 RM(m64 p) { u64 y = MR(p, p.x); return y >= p.m ? y - p.m : y; } m64 construct(u64 z, u64 mod) { m64 p = make_montgomery(mod); p.x = MR(p, (u128)z * p.n2); return p; } m64 plus(m64 p, m64 q) { p.x += q.x - (q.m << 1); p.x = ((i64)p.x < 0 ? p.x + (p.m << 1) : p.x); return p; } m64 minus(m64 p, m64 q) { p.x -= q.x; p.x = ((i64)p.x < 0 ? p.x + (p.m << 1) : p.x); return p; } m64 mult(m64 p, m64 q) { p.x = MR(p, (u128)p.x * q.x); return p; } m64 powmod(m64 p, u64 n) { m64 y = construct(1, p.m); m64 z = p; for (; n; n >>= 1, z = mult(z, z)) if (n & 1) y = mult(y, z); return y; } bool eq(m64 p, m64 q) { return (p.x >= p.m ? p.x - p.m : p.x) == (q.x >= q.m ? q.x - q.m : q.x); } bool not_eq(m64 p, m64 q) { return !eq(p, q); } bool composite(u64 n, const u32* bases, int m) { u64 s = ctz(n - 1); u64 d = (n - 1) >> s; for (int i = 0, j; i < m; ++i) { m64 a = powmod(construct(bases[i], n), d); if (1 == RM(a) || RM(a) == n - 1) continue; for (j = s - 1; j > 0; --j) { a = mult(a, a); if (RM(a) == n - 1) break; } if (j == 0) return true; } return false; } bool is_prime(u64 n) { static const u32 bases[][7] = { {2, 3}, {2, 299417}, {2, 7, 61}, {15, 176006322, (u32)(4221622697)}, {2, 2570940, 211991001, (u32)(3749873356)}, {2, 2570940, 880937, 610386380, (u32)(4130785767)}, {2, 325, 9375, 28178, 450775, 9780504, 1795265022} }; if (n <= 1) return false; if (!(n & 1)) return n == 2; if (n <= 8) return true; int x = 6, y = 7; if (n < 1373653) x = 0, y = 2; else if (n < 19471033) x = 1, y = 2; else if (n < 4759123141) x = 2, y = 3; else if (n < 154639673381) x = y = 3; else if (n < 47636622961201) x = y = 4; else if (n < 3770579582154547) x = y = 5; return !composite(n, bases[x], y); } int main() { int T; scanf("%d", &T); while (T--) { u64 n; scanf("%lu", &n); printf("%lu %d\n", n, (int)is_prime(n)); } return 0; }