{"schema":"vela.problem-packet.v0.1","problem":233,"statement":"Let $d_n=p_{n+1}-p_n$, where $p_n$ is the $n$th prime. Prove that\\[\\sum_{1\\leq n\\leq N}d_n^2 \\ll N(\\log N)^2.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A074741","name":"Sum of squares of gaps between consecutive primes.","terms":"1,5,9,25,29,45,49,65,101,105,141,157,161,177,213,249,253,289,305,309,345,361,397,461,477,481,497,501,517,713,729,765,769","url":"https://oeis.org/A074741"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}