#line 1 "tests/math/is_prime.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/3030" #line 1 "math/montgomery-reduction.hpp" #include namespace libmcr { class montgomery_reduction { __uint128_t N; __uint128_t N_dash; __uint128_t R2; unsigned long long redc(__uint128_t t) { unsigned long long m = N_dash * t; __uint128_t to_ret = (t + N * __uint128_t(m)) >> 64; return to_ret < N ? to_ret : to_ret - N; } public: montgomery_reduction(unsigned long long mod) : N(mod) { N_dash = 0; __uint128_t t = 0; __uint128_t vi = 1; for (int i = 0; i < 64; i++) { if ((t & 1) == 0) { t += N; N_dash += vi; } t >>= 1; vi <<= 1; } R2 = (__uint128_t)(0ull - mod) * (__uint128_t)(0ull - mod) % N; } unsigned long long mult(__uint128_t a, __uint128_t b) { return redc(redc(a * b) * R2); } unsigned long long pow(__uint128_t a, __uint128_t b) { __uint128_t p = redc(R2 * a); __uint128_t x = redc(R2); __uint128_t y = b; while (y) { if (y & 1) { x = redc(x * p); } p = redc(p * p); y >>= 1; } return redc(x); } }; } // namespace libmcr #line 1 "random/xorshift.hpp" #include namespace libmcr { unsigned int xorshift128_32() { static unsigned int x = 123456789, y = 362436069, z = 521288629, w = std::time(nullptr); unsigned int t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); return w; } unsigned long long xorshift128_64() { static unsigned long long x = 123456789, y = 362436069, z = 521288629, w = std::time(nullptr); unsigned long long t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); return w; } } // namespace libmcr #line 3 "math/prime.hpp" #include #include #include namespace libmcr { namespace internal { bool fermat_test(unsigned long long n, const size_t REP_NUM) { montgomery_reduction MR(n); for (size_t rep = 0; rep < REP_NUM; rep++) { unsigned long long a = xorshift128_64() % (n - 1) + 1; if (MR.pow(a, n - 1) != 1) return false; } return true; } bool miller_rabin(unsigned long long n) { if (n <= 1) { return false; } unsigned long long k = 0; unsigned long long m = n - 1; while (!(m & 1)) { k += 1; m >>= 1; } montgomery_reduction MR(n); for (unsigned long long a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { unsigned long long b = MR.pow(a, m); bool flag = false; if (a % n == 0) flag = true; if (b == 1) { flag = true; } else { for (size_t rep2 = 0; rep2 < k; rep2++) { if (b == n - 1) { flag = true; break; } b = MR.mult(b, b); } } if (!flag) return false; } return true; } } // namespace internal bool is_prime(unsigned long long num) { const unsigned long long SMALL_PRIMES[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}; if (num <= 29) { for (unsigned long long i : SMALL_PRIMES) { if (num == i) return true; } return false; } if (!(num & 1)) return false; const unsigned long long PRIME_PRODUCT = 3234846615; if (std::gcd(PRIME_PRODUCT, num) != 1) return false; if (internal::fermat_test(num, 5) && internal::miller_rabin(num)) { return true; } return false; } } // namespace libmcr #line 4 "tests/math/is_prime.test.cpp" #include using namespace std; int main() { int n; cin >> n; for (int i = 0; i < n; i++) { unsigned long long x; cin >> x; if(x<=2){ if(x==2)cout<