#include #include #include #include namespace SPRP { // const std::vector> bases{ {126401071349994536}, // <= 291831 {336781006125, 9639812373923155}, // <= 1050535501 (1e9) {2, 2570940, 211991001, 3749873356}, // <= 47636622961201 (4e13) {2, 325, 9375, 28178, 450775, 9780504, 1795265022} // <= 1e64 }; inline int get_id(long long n) { if (n < 291831) return 0; else if (n < 1050535501) return 1; else if (n < 47636622961201) return 2; else return 3; } } // namespace SPRP // Miller-Rabin primality test // // Complexity: O(lg n) per query struct { long long modpow(__int128 x, __int128 n, long long mod) noexcept { __int128 ret = 1; for (x %= mod; n; x = x * x % mod, n >>= 1) ret = (n & 1) ? ret * x % mod : ret; return ret; } bool operator()(long long n) noexcept { if (n < 2) return false; if (n % 2 == 0) return n == 2; int s = __builtin_ctzll(n - 1); for (__int128 a : SPRP::bases[SPRP::get_id(n)]) { a = modpow(a, (n - 1) >> s, n); bool may_composite = true; if (!a) return true; if (a == 1) continue; for (int r = s; r--; a = a * a % n) if (a == n - 1) may_composite = false; if (may_composite) return false; } return true; } } is_prime; #include int main() { int Q; std::cin >> Q; while (Q--) { long long n; std::cin >> n; std::cout << n << ' ' << is_prime(n) << '\n'; } }