{"schema":"vela.problem-packet.v0.1","problem":1137,"statement":"Let $d_n=p_{n+1}-p_n$, where $p_n$ denotes the $n$th prime. Is it true that\\[\\frac{\\max_{n<x}d_{n}d_{n-1}}{(\\max_{n<x}d_n)^2}\\to 0\\]as $x\\to \\infty$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005250","name":"Record gaps between primes.","terms":"1,2,4,6,8,14,18,20,22,34,36,44,52,72,86,96,112,114,118,132,148,154,180,210,220,222,234,248,250,282,288,292,320,336,354,3","url":"https://oeis.org/A005250"},{"id":"A083550","name":"Product of 2 consecutive prime differences of two successive terms of A001223.","terms":"2,4,8,8,8,8,8,24,12,12,24,8,8,24,36,12,12,24,8,12,24,24,48,32,8,8,8,8,56,56,24,12,20,20,12,36,24,24,36,12,20,20,8,8,24,1","url":"https://oeis.org/A083550"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}