Problem 428

Erdős Problem #428: declared status 'open'. Formalized: yes. Is there a set $A\subseteq \mathbb{N}$ such that, for infinitely many $n$, all of $n-a$ are prime for all $a\in A$ with $0<a<n$ and$$\liminf\frac{\lvert A\cap [1,x]\rvert}{\pi(x)}>0?$$ Prize: no. Tags: number theory, primes.