#include "bits/stdc++.h" #include namespace amylase { using li = long long; li _powmod(const li x, const li n, const li mod) { if (n == 0) { return 1; } li sq = _powmod(x, n / 2, mod); if (n & 1) { return sq * sq % mod * x % mod; } else { return sq * sq % mod; } } bool _miller_rabin(const long long x, const std::vector& witnesses) { if (x <= 1) { return false; } if ((x & 1) == 0) { return x == 2; } long long d = x - 1; long long s = 0; while ((d & 1) == 0) { d >>= 1; s++; } for (const auto& a : witnesses) { if (a % x <= 1) { continue; } bool is_composite = true; is_composite &= _powmod(a, d, x) != 1; long long dd = d; for (int i = 0; i < s; ++i) { is_composite &= _powmod(a, dd, x) != x - 1; dd <<= 1; } if (is_composite) { return false; } } return true; } bool is_prime(const long long x) { return _miller_rabin(x, {2LL, 325LL, 9375LL, 28178LL, 450775LL, 9780504LL, 1795265022LL}); } std::vector factor(long long x) { std::vector factors; long long p = 2; while (p * p <= x) { while (x % p == 0) { factors.emplace_back(p); x /= p; } p++; } if (x > 1) { factors.emplace_back(x); } return factors; } /** * solves ax + by = gcd(a, b) * @param a * @param b * @param x ref to variable to store root x * @param y ref to variable to store root x * @return gcd(a, b) */ long long extgcd(long long a, long long b, long long& x, long long& y) { long long d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } } // namespace amylase using namespace std; typedef long long li; int main() { cin.tie(0); ios::sync_with_stdio(false); li n; cin >> n; for (int i = 0; i < n; ++i) { li x; cin >> x; cout << x << " "; li ispr = amylase::is_prime(x); cout << ispr << '\n'; } return 0; }