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 $N$
Categories: math.GM