#include #include #include #include #include #include #include using std::vector; using Int32 = __int32_t; using Int64 = __int64_t; using Int128 = __int128_t; using ll = long long int; Int128 powmod(Int128 x, Int128 n, ll mod) { Int128 res = 1; while (n > 0) { if (n & 1) { res = (res * x) % mod; } x = x * x % mod; n >>= 1; } return res; } Int128 mulmod(Int128 a, Int128 b, ll mod) { Int128 x = 0, y = a % mod; while (b > 0) { if (b % 2 == 1) { x = (x + y) % mod; } y = (y * 2) % mod; b /= 2; } return x % mod; } ll gcd(ll a, ll b) { if (a < b) std::swap(a, b); while (b > 0) { ll tmp = a; a = b; b = tmp % b; } return a; } inline ll funct(ll x, ll c) { return x * x + c; } bool MillerRabinTest(Int128 n) { constexpr Int128 witness[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 325, 9375, 28178, 450775, 9780504, -1}; if (n == 2) return true; if (n <= 1 || n % 2 == 0) return false; Int128 d = n - 1; int s = 0; while (!(d & 1)) { ++s; d >>= 1; } for (int i = 0; witness[i] != -1 && witness[i] < n; i++) { Int128 y = powmod(witness[i], d, n); if (y == 1) continue; for (int j = 0; j < s - 1 && y != n - 1; j++) y = mulmod(y, y, n); if (y != n - 1) return false; } return true; } int main() { int n; scanf("%d", &n); ll Q; while (n--) { scanf("%lld", &Q); printf("%lld %d", Q, MillerRabinTest(Q)); } // while (Q--) // { // Int a; // scanf("%ld", &a); // vector factor = factorize(a); // printf("%d", static_cast(factor.size())); // for (int i = 0; i < factor.size(); ++i) // { // printf(" %ld", factor[i]); // } // printf("\n"); // } }