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Erdős ProblemsNumber theory

Erdős Problem 1057: Pomerance

Pomerance [Po89] gave a heuristic suggesting that this is the true order of growth, and in fact C(x)=xexp⁡(−(1+o(1))log⁡xlog⁡log⁡log⁡xlog⁡log⁡x)C(x)= x \exp\left(-(1+o(1))\frac{\log x\log\log\log x}{\log\log x}\right).

Number theoryAMS 11

Mathematical statement

Pomerance [Po89] gave a heuristic suggesting that this is the true order of growth, and in fact C(x)=xexp⁡(−(1+o(1))log⁡xlog⁡log⁡log⁡xlog⁡log⁡x)C(x)= x \exp\left(-(1+o(1))\frac{\log x\log\log\log x}{\log\log x}\right).

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_1057.variants.pomerance

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_1057.variants.pomerance :    answer(sorry) ↔ Tendsto (fun x ↦      -(Real.log (carmichaelCounting x / x) * Real.log (Real.log x)) /      (Real.log x * Real.log (Real.log (Real.log x)))) atTop (𝓝 1) := 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

Pinned Formal Conjectures sourceformalizationerdosproblems.com/1057background