{"schema":"vela.problem-packet.v0.1","problem":779,"statement":"Let $n&#62; 1$ and $p_1&#60;\\cdots&#60;p_n$ denote the first $n$ primes. Let $P=\\prod_{1\\leq i\\leq n}p_i$. Does there always exist some prime $p$ with $p_n&#60;p&#60;P$ such that $P+p$ is prime?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005235","name":"Fortunate numbers: least m > 1 such that m + prime(n)# is prime, where p# denotes the product of all primes <= p.","terms":"3,5,7,13,23,17,19,23,37,61,67,61,71,47,107,59,61,109,89,103,79,151,197,101,103,233,223,127,223,191,163,229,643,239,157,1","url":"https://oeis.org/A005235"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}