Why is there no speed up when using OpenMP to generate random numbers?

I am looking to run a type of monte carlo simulations which require the generation of random numbers, and a set of instructions based on those random numbers.

I wish to make use of parallel processing but when testing my code (written in C) there seems to be an inverse speed up with more cores! I'm not sure what I could be doing wrong. I then copied the code form another answer and still get this effect.

The code slightly modified form the answer is

#define NRANDS 1000000
int main() {

    int a[NRANDS];

    #pragma omp parallel default(none) shared(a)
    {
        int i;
        unsigned int myseed = omp_get_thread_num();
        #pragma omp for
        for(i=0; i<NRANDS; i++)
                a[i] = rand_r(&myseed);
    }
    double sum = 0.;
    for (long int i=0; i<NRANDS; i++) {
        sum += a[i];
    }
    printf("sum = %lf\n", sum);

    return 0;
}

where I have just then run the time command in terminal in order to time how long it takes to run. I varied the number of threads allowed using export OMP_NUM_THREADS=2. The output of my terminal is:

Thread total: 1
sum = 1074808568711883.000000
real    0m0,041s
user    0m0,036s
sys 0m0,004s

Thread total: 2
sum = 1074093295878604.000000
real    0m0,037s
user    0m0,058s
sys 0m0,008s

Thread total: 3
sum = 1073700114076905.000000
real    0m0,032s
user    0m0,061s
sys 0m0,010s

Thread total: 4
sum = 1073422298606608.000000

real    0m0,035s
user    0m0,074s
sys 0m0,024s