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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 233

A conjecture by Heath-Brown: The sum of squares of the first NN gaps between consecutive primes behaves like N(logN)2N * (log N)^2.

Mathematical statement

A conjecture by Heath-Brown: The sum of squares of the first NN gaps between consecutive primes behaves like N(logN)2N * (log N)^2.

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_233

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_233 :    (fun N => ((∑ n  Finset.range N, (primeGap n) ^ 2) : )) =O[atTop] fun N => N * (log N)^2 := 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