{"schema":"vela.problem-packet.v0.1","problem":386,"statement":"Let $2\\leq k\\leq n-2$. Can $\\binom{n}{k}$ be the product of consecutive primes infinitely often? For example\\[\\binom{21}{2}=2\\cdot 3\\cdot 5\\cdot 7.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A280992","name":"Squarefree triangular numbers that are products of consecutive primes.","terms":"1,3,6,15,105,210,255255","url":"https://oeis.org/A280992"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}