{"schema":"vela.problem-packet.v0.1","problem":313,"statement":"Are there infinitely many solutions to\\[\\frac{1}{p_1}+\\cdots+\\frac{1}{p_k}=1-\\frac{1}{m},\\]where $m\\geq 2$ is an integer and $p_1<\\cdots<p_k$ are distinct primes?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_6ba6154f2ce22b91","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=none) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A054377","name":"Primary pseudoperfect numbers: numbers k > 1 such that 1/k + sum 1/p = 1, where the sum is over the primes p | k.","terms":"2,6,42,1806,47058,2214502422,52495396602,5998279018951962402","url":"https://oeis.org/A054377"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}