{"schema":"vela.problem-packet.v0.1","problem":382,"statement":"Let $u\\leq v$ be such that the largest prime dividing $\\prod_{u\\leq m\\leq v}m$ appears with exponent at least $2$. Is it true that $v-u=v^{o(1)}$? Can $v-u$ be arbitrarily large?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A388850","name":"Initial term of first maximal bad interval of width n, i.e., initial term of the first run of exactly n+1 consecutive integers in A388654; or 0 if no such interval exists.","terms":"4,8,48,1680,76725,332925,7474752,4541154,75047565","url":"https://oeis.org/A388850"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}