Formal target: Corpus.WikipediaAndrica.andrica_conjecture
**Andrica's conjecture** The inequality $\sqrt{p_{n+1}}-\sqrt{p_n} < 1$ holds for all $n$, where $p_n$ is the $n$-th prime number.
Exact formal statement
∀ (n : Nat),
LT.lt.{0}
(HSub.hSub.{0, 0, 0} (Nat.cast.{0} (Nat.nth Nat.Prime (HAdd.hAdd.{0, 0, 0} n 1))).sqrt
(Nat.cast.{0} (Nat.nth Nat.Prime n)).sqrt)
1This target is a formal statement, not a proof of the problem.
Environment availability: available.