#include using u32 = unsigned int; using u64 = unsigned long long; using u128 = __uint128_t; template bool is_prime_impl(const Uint &n, const Uint *witness, BinOp modmul) { if (n == 2) return true; if (n < 2 || n % 2 == 0) return false; const Uint m = n - 1, d = m / (m & -m); auto modpow = [&](Uint a, Uint b) { Uint res = 1; for (; b; b /= 2) { if (b & 1) res = modmul(res, a); a = modmul(a, a); } return res; }; auto suspect = [&](Uint a, Uint t) { a = modpow(a, t); while (t != n - 1 && a != 1 && a != n - 1) { a = modmul(a, a); t = modmul(t, 2); } return a == n - 1 || t % 2 == 1; }; for (const Uint *w = witness; *w; w++) { if (*w % n != 0 && !suspect(*w, d)) return false; } return true; } bool is_prime(const u128 &n) { assert(n < 1ULL << 63); if (n < 1ULL << 32) { // n < 2^32 constexpr u64 witness[] = {2, 7, 61, 0}; auto modmul = [&](u64 a, u64 b) { return a * b % n; }; return is_prime_impl(n, witness, modmul); } else { // n < 2^63 constexpr u128 witness[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022, 0}; // if u128 is available auto modmul = [&](u128 a, u128 b) { return a * b % n; }; // otherwise // auto modmul = [&](u64 a, u64 b) { // u64 res = 0; // for (; b; b /= 2) { // if (b & 1) res = (res + a) % n; // a = (a + a) % n; // } // return res; // }; return is_prime_impl(n, witness, modmul); } } using namespace std; int main() { cin.tie(0); ios::sync_with_stdio(0); int n; cin >> n; while (n--) { u64 x; cin >> x; cout << x << ' ' << is_prime(x) << '\n'; } }