A simple estimate of the number of Goldbach pairs for N

Using the fact that the number of combinations $p_1$, $p_2$, where $p_1$ and $p_2$ are odd primes, with $p_1\le p_2$ and $p_1+p_2\le 2N$ is equal to the total number of Goldbach pairs for all the even integers from 6 to $2N$, we derive in a simple way an accurate estimate of the number of Goldbach pairs for $N$