Source labels openChecked July 26, 2026

Erdős Problem 15

Is it true that $\sum_{n=1}^\infty(-1)^n\frac{n}{p_n}$ converges, where $p_n$ is the sequence of primes?

Mathematical statement

Is it true that $\sum_{n=1}^\infty(-1)^n\frac{n}{p_n}$ converges, where $p_n$ is the sequence of primes?

Note: In the problem statement, $p_n$ is the $n$ -th prime, indexed such that $p_1=2, p_2=3, \ldots$ . We 0-index here to reflect how Nat.nth works.

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_15

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_15 : answer(sorry) ↔    Summable (fun k : ℕ => (-1 : ℚ) ^ (k + 1) * (k + 1) / (k.nth Nat.Prime)) := 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/15background