{"schema":"vela.problem-packet.v0.1","problem":457,"statement":"Is there some $\\epsilon>0$ such that there are infinitely many $n$ where all primes $p\\leq (2+\\epsilon)\\log n$ divide\\[\\prod_{1\\leq i\\leq \\log n}(n+i)?\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A391668","name":"Table read by antidiagonals. T(n,k) is the least number coprime to all numbers in [n+1, n+k].","terms":"3,5,2,5,5,3,7,7,3,2,7,7,7,7,5,11,11,11,11,5,2,11,11,11,11,5,3,3,11,11,11,11,5,5,5,2,11,11,11,11,11,11,7,7,3,13,13,13,13,","url":"https://oeis.org/A391668"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}