{"schema":"vela.problem-packet.v0.1","problem":1065,"statement":"Are there infinitely many primes $p$ such that $p=2^kq+1$ for some prime $q$ and $k\\geq 0$? Or $p=2^k3^lq+1$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A074781","name":"Primes of the form p*2^k + 1 for any k and any prime p.","terms":"3,5,7,11,13,17,23,29,41,47,53,59,83,89,97,107,113,137,149,167,173,179,193,227,233,257,263,269,293,317,347,353,359,383,38","url":"https://oeis.org/A074781"},{"id":"A339465","name":"Primes p such that (p-1)/gpf(p-1) = 2^q * 3^r with q, r >= 1, where gpf(m) is the greatest prime factor of m, A006530.","terms":"19,31,37,43,61,67,73,79,103,109,127,139,157,163,181,199,223,229,241,271,277,283,307,313,337,349,367,373,379,397,409,433,","url":"https://oeis.org/A339465"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}