{"schema":"vela.problem-packet.v0.1","problem":1143,"statement":"Let $p_1<\\cdots<p_u$ be primes and let $k\\geq 1$. Let $F_k(p_1,\\ldots,p_u)$ be such that every interval of $k$ positive integers contains at least $F_k(p_1,\\ldots,p_u)$ multiples of at least one of the $p_i$.Estimate $F_k(p_1,\\ldots,p_u)$, particularly in the range $k=\\alpha p_u$ for constant $\\alpha>2$.","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)"}