{"schema":"vela.problem-packet.v0.1","problem":1072,"statement":"For any prime $p$, let $f(p)$ be the least integer such that $f(p)!+1\\equiv 0\\pmod{p}$.Is it true that there are infinitely many $p$ for which $f(p)=p-1$?Is it true that $f(p)/p\\to 0$ for almost all $p$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A072937","name":"Least k such that prime(n) appears in factorization of k! + 1.","terms":"2,4,3,5,12,16,9,14,18,30,36,40,21,23,52,15,8,18,7,72,23,13,88,96,100,6,106,86,112,63,65,16,16,50,150,156,81,166,172,89,1","url":"https://oeis.org/A072937"},{"id":"A073944","name":"a(n) is the smallest m such that n-th prime divides m! + 1.","terms":"1,2,4,3,5,12,16,9,14,18,30,36,40,21,23,52,15,8,18,7,72,23,13,88,96,100,6,106,86,112,63,65,16,16,50,150,156,81,166,172,89","url":"https://oeis.org/A073944"},{"id":"A154554","name":"Primes p such that m=p-1 is the least number such that p divides m!+1.","terms":"2,3,5,13,17,31,37,41,53,73,89,97,101,107,113,151,157,167,173,181,197,211,223,229,241,281,283,313,331,337,349,353,373,409","url":"https://oeis.org/A154554"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}