I tried parallelizing a code snippet with OpenMP, it turns out that engaing OpenMP takes 25X time for the program to finish. Is there anything wrong? How can I optimize it?

#include <iostream>
#include <cmath>
#include <random>
#include <chrono>
#include <cstdlib>
#include <omp.h>

using namespace std;

int main() {
        unsigned long long black_square = 1, digit_square = 13;
        //auto n = ((black_square)<<11) * static_cast<unsigned long long>(pow(digit_square,10));
        auto n = static_cast<unsigned long long>(1e9);
        srand(0);
        int tmp = 0;
        std::random_device rd;  // Will be used to obtain a seed for the random number engine
        std::mt19937 gen(rd()); // Standard mersenne_twister_engine seeded with rd()
        std::uniform_int_distribution<> distrib(1, 6);

        auto tStart = std::chrono::high_resolution_clock::now();
//#pragma omp parallel for schedule(static) reduction(+:tmp)
#pragma omp parallel for schedule(static) reduction(+:tmp) num_threads(8)
        for (unsigned long long i=0; i<n; i++) tmp = (tmp+(5==rand()%6))%static_cast<int>(1e9);
        //for (unsigned long long i=0; i<n; i++) tmp = (tmp+(5==distrib(gen)))%static_cast<int>(1e9);
        tmp%=static_cast<int>(1e9);
        auto tEnd = std::chrono::high_resolution_clock::now();

        cout << tmp << " obtained after " << n << " iterations in " << (tEnd-tStart).count()/1e9 << "s." << endl;
        return 0;
}

The code is compiled by g++ -o a.out -O3 -std=c++11 -fopenmp tmp.cpp where g++ has version 8.5.0 20210514. The OS is RHEL8.9 and there are 20 Intel Xeon CPUs at 2.593GHz.

The serial code on average runs in 7.4s while the parallel code on average runs in 180s. Options -O3, -O2, -O1 have similiar results. Random generator mt19937 could reduce the performance gap significantly, but the parallel code is still much slower than the serial version. Increasing or decreasing n leads to similar results as well.