The second Hardy–Littlewood conjecture for the prime-counting function

Let $\pi(t)$ denote the number of primes at most $t$, and let $x,y\geq 2$. Second Hardy–Littlewood conjecture.

$$\pi(x+y)\leq\pi(x)+\pi(y).$$

This is a classical subadditivity conjecture for the prime-counting function and remains an open problem.