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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 950: Weaker Pi

Erdős writes that a 'weaker conjecture which is perhaps not quite inaccessible' is that, for every ϵ>0\epsilon>0, if xx is sufficiently large there exists y<xy<x such that π(x)<π(y)+ϵπ(xy)\pi(x)< \pi(y)+\epsilon \pi(x-y). Compare this to [855].

Mathematical statement

Erdős writes that a 'weaker conjecture which is perhaps not quite inaccessible' is that, for every ϵ>0\epsilon>0, if xx is sufficiently large there exists y<xy<x such that π(x)<π(y)+ϵπ(xy)\pi(x)< \pi(y)+\epsilon \pi(x-y). Compare this to [855].

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_950.variants.weaker_pi

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_950.variants.weaker_pi :    answer(sorry)   ε > 0, ᶠ x in atTop,  y < x,      (π x : ) < (π y : ) + ε * (π (x - y) : ) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References