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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 855

Erdős Problem 855 (Segal's conjecture): π(x+y)π(x)+π(y)\pi(x + y) \le \pi(x) + \pi(y) for sufficiently large x,yx, y.

Mathematical statement

Erdős Problem 855 (Segal's conjecture): π(x+y)π(x)+π(y)\pi(x + y) \le \pi(x) + \pi(y) for sufficiently large x,yx, y.

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_855

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_855 : answer(sorry)     ᶠ x in atTop, ᶠ y in atTop, π (x + y)  π x + π 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