372.lean`

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L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 372

Reference: erdosproblems.com/372

Conjectured by Erdős and Pomerance. Proved by Balog, who showed the stronger quantitative result that this holds for $\gg \sqrt{x}$ many $n\leq x$, for all large $x$.

Imports (1)

FormalConjecturesUtil

theorem Erdos372.erdos_372 Let $P(n)$ denote the largest prime factor of $n$ sorry line 38 source
Source documentation
Let $P(n)$ denote the largest prime factor of $n$. There are infinitely many $n$ such that $P(n)>P(n+1)>P(n+2)$.

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, And, GT.gt, Nat.maxPrimeFac, HAdd.hAdd, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_372 :
    {n : ℕ | Nat.maxPrimeFac n > Nat.maxPrimeFac (n + 1) ∧
      Nat.maxPrimeFac (n + 1) > Nat.maxPrimeFac (n + 2)}.Infinite := by
…
```
Mentions: Nat.maxPrimeFac