{"schema":"vela.problem-packet.v0.1","problem":427,"statement":"Is it true that, for every $n$ and $d$, there exists $k$ such that\\[d \\mid p_{n+1}+\\cdots+p_{n+k},\\]where $p_r$ denotes the $r$th prime?","status":"solved","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)"}