Formal target: Corpus.Erdos208.erdos_208.variants.log_bound
In [Er79] Erdős says perhaps $s_{n+1} - s_n \ll \log s_n$, but he is 'very doubtful'.
Exact formal statement
Asymptotics.IsBigO.{0, 0, 0} Filter.atTop.{0}
(fun n =>
HSub.hSub.{0, 0, 0} (Nat.cast.{0} (Corpus.Erdos208.erdos208.s (HAdd.hAdd.{0, 0, 0} n 1)))
(Nat.cast.{0} (Corpus.Erdos208.erdos208.s n)))
fun n => Real.log (Nat.cast.{0} (Corpus.Erdos208.erdos208.s n))This target is a formal statement, not a proof of the problem.
Environment availability: available.