  The binary Goldbach conjecture asserts that every even integer greater than
$4$ is the sum of two primes. In a preceding paper we have proved that there
exists a positive integer $K_\alpha$ such that every even integer $x > p_k^2$
can be expressed as the sum of two primes, where $p_k$ is the $k$th prime
number and $k > K_\alpha$. In this paper we provide an estimation for
$K_\alpha$, and from this result it follows that the binary Goldbach conjecture
is true.
