OPEN
This is open, and cannot be resolved with a finite computation.
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\[\liminf\frac{\lvert A\cap [1,x]\rvert}{\pi(x)}>0?\]
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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #428, https://www.erdosproblems.com/428, accessed 2026-04-11
