Number of primes $< n^3$

formal-conjectures · oeis · ams-11

Number of primes strictly less than $n^3$.

Conjecture (i): for any integer $k > 2$, the sequence $\pi(n^k)/n^k$ ($n = 2, 3, \ldots$) is strictly
decreasing, where $\pi(x)$ denotes the number of primes not exceeding $x$.
- Zhi-Wei Sun, Oct 17 2015

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/A038098
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/38098.lean
Local target: Corpus.OEIS38098.conjecture1
Source SHA-256: a487f779f6bbee20a8ffab8cda23212efc92cd31320d8da5dcab4c3497870b12
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