The natural-boundary conjecture for the Goldbach Dirichlet series

Let $G_2(n)=\sum_{k+m=n}\Lambda(k)\Lambda(m)$ for positive integers $n$, where $\Lambda$ is the von Mangoldt function, and define

$$\Phi_2(s)=\sum_{n=1}^{\infty}\frac{G_2(n)}{n^s}.$$

Under the Riemann hypothesis, $\Phi_2(s)$ admits a meromorphic continuation to $\Re s>1$. Natural-boundary conjecture. The line $\Re s=1$ is the natural boundary of $\Phi_2(s)$. This conjecture concerns the obstruction to continuing the Goldbach Dirichlet series beyond the half-plane where its meromorphic continuation is known under the Riemann hypothesis.