{"schema":"vela.problem-packet.v0.1","problem":428,"statement":"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?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}