Source labels openChecked July 26, 2026

Erdős Problem 1106: Ii

Let $p(n)$ be the partition number of $n$ and $F(n)$ be the number of distinct prime factors of $∏_{i= 1} ^ {n} p(n)$ , $F(n)>n$ for sufficiently large $n$ .

Number theory AMS 11

Mathematical statement

Let $p(n)$ be the partition number of $n$ and $F(n)$ be the number of distinct prime factors of $∏_{i= 1} ^ {n} p(n)$ , $F(n)>n$ for sufficiently large $n$ .

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_1106.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1106.parts.ii :    answer(sorry) ↔ ∀ᶠ n in atTop, #(∏ i ∈ Icc 1 n, p i).primeFactors > n := 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 sourceformalization erdosproblems.com/1064background