#include /** * @title 128-bit int * @docs int128.md */ #ifdef __SIZEOF_INT128__ using uint128_t = __uint128_t; using int128_t = __int128_t; #else #include using uint128_t = boost::multiprecision::uint128_t; using int128_t = boost::multiprecision::int128_t; #endif class MillerRabin{ static inline uint64_t power(uint64_t a, uint64_t b, uint64_t p){ uint64_t ret = 1; while(b > 0){ if(b & 1) ret = static_cast(ret) * a % p; a = static_cast(a) * a % p; b >>= 1; } return ret; } static inline uint64_t power32(uint64_t a, uint64_t b, uint64_t p){ uint64_t ret = 1; while(b > 0){ if(b & 1) ret = ret * a % p; a = a * a % p; b >>= 1; } return ret; } static inline bool is_composite(uint64_t a, uint64_t p, int s, uint64_t d){ uint64_t x = p < std::numeric_limits::max() ? power32(a, d, p) : power(a, d, p); if(x == 1) return false; for(int i = 0; i < s; ++i){ if(x == p-1) return false; if(x < std::numeric_limits::max()){ x = x * x % p; }else{ x = static_cast(x) * x % p; } } return true; } public: static inline bool is_prime(uint64_t n){ if(n <= 1) return false; if(n == 2) return true; if(n % 2 == 0) return false; int s = 0; uint64_t d = n-1; while((d & 1) == 0){ s += 1; d >>= 1; } if(n < 4759123141){ for(uint64_t x : {2, 7, 61}){ if(x < n and is_composite(x, n, s, d)) return false; } return true; } for(uint64_t x : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}){ if(x < n and is_composite(x, n, s, d)) return false; } return true; } }; int main(){ std::cin.tie(0); std::ios::sync_with_stdio(false); int N; std::cin >> N; for(int i = 0; i < N; ++i){ int64_t x; std::cin >> x; std::cout << x << " " << MillerRabin::is_prime(x) << std::endl; } return 0; }