Source labels openChecked July 26, 2026

Erdős Problem 251

Is $\sum_{n=1}^\infty \frac{p_n}{2^n}$ irrational? Here $p_n$ is the $n$ -th prime ( $p_1=2, p_2=3, \dots$ ).

Number theory AMS 11

Mathematical statement

Is $\sum_{n=1}^\infty \frac{p_n}{2^n}$ irrational? Here $p_n$ is the $n$ -th prime ( $p_1=2, p_2=3, \dots$ ).

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_251

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_251 : answer(sorry) ↔ Irrational (∑' n : ℕ, (Nat.nth Nat.Prime n) / (2 ^ 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/251background