{"schema":"vela.problem-packet.v0.1","problem":1113,"statement":"A positive odd integer $m$ such that none of $2^km+1$ are prime for $k\\geq 0$ is called a Sierpinski number. We say that a set of primes $P$ is a covering set for $m$ if every $2^km+1$ is divisible by some $p\\in P$.Are there Sierpinski numbers with no finite covering set of primes?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_3159933b2b9597a8","kind":"dead_end","claim":"attempted via frontier 'difference/covering' (transfer_strength=weak) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A076336","name":"(Provable) Sierpiński numbers: odd numbers n such that for all k >= 1 the numbers n*2^k + 1 are composite.","terms":"78557,271129,271577,322523,327739,482719,575041,603713,903983,934909,965431,1259779,1290677,1518781,1624097,1639459,1777","url":"https://oeis.org/A076336"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}