{"schema":"vela.problem-packet.v0.1","problem":219,"statement":"Are there arbitrarily long arithmetic progressions of primes?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005115","name":"Let i, i+d, i+2d, ..., i+(n-1)d be an n-term arithmetic progression of primes; choose the one which minimizes the last term; then a(n) = last term i+(n-1)d.","terms":"2,3,7,23,29,157,907,1669,1879,2089,249037,262897,725663,36850999,173471351,198793279,4827507229,17010526363,83547839407,","url":"https://oeis.org/A005115"},{"id":"A113827","name":"Initial terms associated with the arithmetic progressions of primes in A005115.","terms":"2,2,3,5,5,7,7,199,199,199,110437,110437,4943,31385539,115453391,53297929,3430751869,4808316343,8297644387,214861583621,5","url":"https://oeis.org/A113827"},{"id":"A123556","name":"Number of elements in longest possible arithmetic progression of primes with difference n.","terms":"2,3,2,3,2,5,1,3,2,3,2,5,1,3,2,2,2,4,1,3,2,2,1,4,1,2,2,3,2,6,1,2,1,3,2,4,1,3,2,3,2,5,1,2,2,2,1,5,1,3,2,2,1,4,1,2,2,2,2,6,","url":"https://oeis.org/A123556"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}