{"schema":"vela.problem-packet.v0.1","problem":4,"statement":"Is it true that, for any $C&#62;0$, there are infinitely many $n$ such that\\[p_{n+1}-p_n&#62; C\\frac{\\log\\log n\\log\\log\\log\\log n}{(\\log\\log \\log n)^2}\\log n?\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A002386","name":"Primes (lower end) with record gaps to the next consecutive prime: primes p(k) where p(k+1) - p(k) exceeds p(j+1) - p(j) for all j < k.","terms":"2,3,7,23,89,113,523,887,1129,1327,9551,15683,19609,31397,155921,360653,370261,492113,1349533,1357201,2010733,4652353,170","url":"https://oeis.org/A002386"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}