Integer part of $\mathrm{prime}(n)/\pi(n)$

formal-conjectures · oeis · ams-11

Here $\mathrm{prime}(n)$ is the $n$-th prime number, and $\pi(n)$ is the prime-counting function.

Conjecture: As $n \rightarrow \infty$, there are infinitely many n's such that
$a(n)$ is greater than $a(n+1)$.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A111114
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/111114.lean
Local target: Corpus.OEIS111114.conjecture
Source SHA-256: 59293ff04409b7656340f0f0025797803f421a8832c4a4cb6c98c9873a072bd9
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record