Why isn't the second loop faster?

I just read this intro to parallel processing with openMP.

I tried the following simple code

#include <iostream>
#include <ctime>
#include <vector>

int main()
{
        // Create an object just to allow the following loops to do something
        std::vector<int> a;
        a.reserve(2000);

        // First single threaded loop
        std::clock_t begin;
        std::clock_t end;
        begin = std::clock();
        double elapsed_secs;

        for(int n=0; n<1000000000; ++n)
        {
                if (n%100000000 == 0) a.push_back(n);
        }

        end = std::clock();

        elapsed_secs = double(end - begin) / CLOCKS_PER_SEC;
        std::cout << "Time for single thread loop: " << elapsed_secs << std::endl;

        // Second multithreaded loop
        begin = std::clock();
        #pragma omp parallel for
        for(int n=0; n<1000000000; ++n)
        {
                if (n%100000000 == 0) a.push_back(n);
        }

        end = std::clock();
        elapsed_secs = double(end - begin) / CLOCKS_PER_SEC;
        std::cout << "Time for multi thread loop: " << elapsed_secs << std::endl;

        return 0;
}

which has been compiled with g++ -std=c++11 -o a a.cpp -fopenmp which outputs

Time for single thread loop: 3.9438
Time for multi thread loop: 3.94977

• Do I misunderstand how to parallelize in C++
• Do I misunderstand how to compile?
• Is the code parallelize but the improvement in speed is not-noticable for whatever reason?

Note that I have 12 cores (and no big process currently running) on my machine.