{"schema":"vela.problem-packet.v0.1","problem":853,"statement":"Let $d_n=p_{n+1}-p_n$, where $p_n$ is the $n$th prime. Let $r(x)$ be the smallest even integer $t$ such that $d_n=t$ has no solutions for $n\\leq x$.Is it true that $r(x)\\to \\infty$? Or even $r(x)/\\log x \\to \\infty$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A001223","name":"Prime gaps: differences between consecutive primes.","terms":"1,2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2,10,2,6,6,4,6,6,2,10,2,4,2,12,12,4,2,4,6,2,10,6,6,6,2,","url":"https://oeis.org/A001223"},{"id":"A390769","name":"Least even positive integer k that does not appear in the first n prime gaps.","terms":"2,4,4,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,10,10,10,10,10,10,10,10,10,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16","url":"https://oeis.org/A390769"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}