{"schema":"vela.problem-packet.v0.1","problem":680,"statement":"Is it true that, for all sufficiently large $n$, there exists some $k$ such that\\[p(n+k)>k^2+1,\\]where $p(m)$ denotes the least prime factor of $m$?Can one prove this is false if we replace $k^2+1$ by $e^{(1+\\epsilon)\\sqrt{k}}+C_\\epsilon$, for all $\\epsilon>0$, where $C_\\epsilon>0$ is some constant?","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)"}