Source labels openChecked July 26, 2026

Erdős Problem 726

As $n\to \infty$ ranges over integers $\sum_{p\leq n}1_{n\in (p/2,p)\pmod{p}}\frac{1}{p}\sim \frac{\log\log n}{2}$ ?

Number theory AMS 11

Mathematical statement

As $n\to \infty$ ranges over integers $\sum_{p\leq n}1_{n\in (p/2,p)\pmod{p}}\frac{1}{p}\sim \frac{\log\log n}{2}$ ?

A conjecture of Erdős, Graham, Ruzsa, and Straus [EGRS75].

By $n\in (p/2,p)\pmod{p}$ we mean $n\equiv r\pmod{p}$ for some integer $r$ with $p/2<r<p$ .

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_726

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_726 :    answer(sorry) ↔      (fun n : ℕ ↦ ∑ p ∈ (range (n + 1)).filter          (fun p : ℕ ↦ p.Prime ∧ (p : ℝ) / 2 < (n % p : ℝ)),        (1 : ℝ) / (p : ℝ))      ~[atTop] (fun n : ℕ ↦ Real.log (Real.log (n : ℝ)) / 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/726background