  Using the fact that the number of combinations $p_{1}$, $p_{2}$, where
$p_{1}$ and $p_{2}$ are odd primes, with $p_{1} \leq p_{2}$ and $p_{1} + p_{2}
\leq 2N$ 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 $N$
