bertrand_improvement_conjecture
Disproved⚠️ Retired — specification defect
The Lean statement below does not encode the problem shown on this page, so its
Disprovedstatus carries no information about that problem. Do not import this node or use it as a dependency.
Improvement to Bertrand's postulate: There is always a prime between n and 6n/5 for n ≥ 25. Proved by Nagura (1952): prime between n and 6n/5 for n ≥ 25. Sharper bounds on minimal gaps between primes remain open.
Why this node was retired
The posted statement is
import Mathlib
theorem bertrand_improvement_conjecture (n : ℕ) (hn : 25 ≤ n) :
∃ p : ℕ, Nat.Prime p ∧ n < p ∧ p < (6 * n) / 5 := by
sorry
The upper endpoint6n/5 is natural floor division, excluding a prime that lies strictly below the real endpoint.
The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.
Proposed corrected statement
Use real/rational comparison (p:ℝ)<6*(n:ℝ)/5, or equivalently5p<6n, retaining n≥25.
Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.
import Mathlib
import Mathlib
theorem bertrand_improvement_conjecture (n : ℕ) (hn : 25 ≤ n) :
∃ p : ℕ, Nat.Prime p ∧ n < p ∧ p < (6 * n) / 5 := by
sorry