Problem p00509 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>

using namespace std;

#define fst(t) std::get<0>(t)
#define snd(t) std::get<1>(t)
#define thd(t) std::get<2>(t)
#define unless(p) if (!(p))
#define until(p) while (!(p))

using ll = long long;
using ull = unsigned long long;
using P = std::tuple<int, int>;

const int dx[8] = {-1, 1, 0, 0, -1, -1, 1, 1},
          dy[8] = {0, 0, -1, 1, -1, 1, -1, 1};

int N, C, D;
ll powers[19], numbers101[9];
std::mt19937 engine;

ll product(ll a, ll b, ll m) {
  ll res = 0ll;

  for (int i = 60; i >= 0; i -= 4) {
    res = (res * 16 + a * (b >> i & 15)) % m;
  }

  return res;
}

template <typename T> T expt(T a, T n, T mod = std::numeric_limits<T>::max()) {
  T res = 1;
  while (n) {
    if (n & 1) {
      res = product(res, a, mod);
    }
    a = product(a, a, mod);
    n >>= 1;
  }
  return res;
}

inline ll isPrime(ll x) {
  if (x % 2 == 0) {
    return x == 2;
  }

  ll d = x - 1;
  int s = 0;
  while (d % 2 == 0) {
    ++s;
    d /= 2;
  }

  static int t = 10;
  for (int i = 0; i < t; ++i) {
    ll a = engine() % x, po = expt(a, d, x);

    bool flag = po == 1;
    for (int j = 0; j < s; ++j) {
      if (po == x - 1) {
        flag = true;
        break;
      }
      po = product(po, po, x);
    }

    if (!flag) {
      return false;
    }
  }

  return true;
}

inline ll reverseNumber(ll x) {
  std::string s = std::to_string(x);
  reverse(s.begin(), s.end());
  return std::stoll(s) * powers[N - 1 - s.size()];
}

int main() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);

  for (int i = 0; i <= 18; ++i) {
    powers[i] = expt(10ll, 1ll * i);
  }

  std::cin >> N >> C;

  D = 2 * N + (C >= 0) - 1;

  if (N >= 2 && C == -1) {
    std::cout << std::string(D + 1, '9') << std::endl;
    return 0;
  }

  for (int i = 0; i < N; ++i) {
    numbers101[i] = powers[D - i] + powers[i];
  }

  bool founded = false;
  ll res = -1ll;
  for (int i = 9; !founded && i >= 1; i -= 2) {
    for (ll j = powers[N - 1] - 1; !founded && j >= 0; --j) {
      ll x = (C >= 0 ? powers[N] * C : 0ll) + numbers101[0] * i +
             (j * powers[N - 1 + (C >= 0 ? 1 : 0)] + reverseNumber(j)) * 10;

      if (isPrime(x)) {
        founded = true;
        res = x;
      }
    }
  }

  if (res >= 0) {
    std::cout << res << std::endl;
  } else {
    std::cout << std::string(D + 1, '9') << std::endl;
  }
}

Fixed submission:
#include <bits/stdc++.h>

using namespace std;

#define fst(t) std::get<0>(t)
#define snd(t) std::get<1>(t)
#define thd(t) std::get<2>(t)
#define unless(p) if (!(p))
#define until(p) while (!(p))

using ll = long long;
using ull = unsigned long long;
using P = std::tuple<int, int>;

const int dx[8] = {-1, 1, 0, 0, -1, -1, 1, 1},
          dy[8] = {0, 0, -1, 1, -1, 1, -1, 1};

int N, C, D;
ll powers[19], numbers101[9];
std::mt19937 engine;

ll product(ll a, ll b, ll m) {
  ll res = 0ll;

  for (int i = 60; i >= 0; i -= 4) {
    res = (res * 16 + a * (b >> i & 15)) % m;
  }

  return res;
}

template <typename T> T expt(T a, T n, T mod = std::numeric_limits<T>::max()) {
  T res = 1;
  while (n) {
    if (n & 1) {
      res = product(res, a, mod);
    }
    a = product(a, a, mod);
    n >>= 1;
  }
  return res;
}

inline ll isPrime(ll x) {
  if (x % 2 == 0) {
    return x == 2;
  }

  ll d = x - 1;
  int s = 0;
  while (d % 2 == 0) {
    ++s;
    d /= 2;
  }

  static int t = 10;
  for (int i = 0; i < t; ++i) {
    ll a = engine() % x, po = expt(a, d, x);

    bool flag = po == 1;
    for (int j = 0; j < s; ++j) {
      if (po == x - 1) {
        flag = true;
        break;
      }
      po = product(po, po, x);
    }

    if (!flag) {
      return false;
    }
  }

  return true;
}

inline ll reverseNumber(ll x) {
  std::string s = std::to_string(x);
  reverse(s.begin(), s.end());
  return std::stoll(s) * powers[N - 1 - s.size()];
}

int main() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);

  for (int i = 0; i <= 18; ++i) {
    powers[i] = expt(10ll, 1ll * i);
  }

  std::cin >> N >> C;

  D = 2 * N + (C >= 0) - 1;

  if (N >= 2 && C < 0) {
    std::cout << std::string(D + 1, '9') << std::endl;
    return 0;
  }

  for (int i = 0; i < N; ++i) {
    numbers101[i] = powers[D - i] + powers[i];
  }

  bool founded = false;
  ll res = -1ll;
  for (int i = 9; !founded && i >= 1; i -= 2) {
    for (ll j = powers[N - 1] - 1; !founded && j >= 0; --j) {
      ll x = (C >= 0 ? powers[N] * C : 0ll) + numbers101[0] * i +
             (j * powers[N - 1 + (C >= 0 ? 1 : 0)] + reverseNumber(j)) * 10;

      if (isPrime(x)) {
        founded = true;
        res = x;
      }
    }
  }

  if (res >= 0) {
    std::cout << res << std::endl;
  } else {
    std::cout << std::string(D + 1, '9') << std::endl;
  }
}