Source labels openChecked July 26, 2026

Erdős Problem 358: Prime Set Density Representation

When $A =\{a_1 < \cdots\}$ corresponds to the set of primes, it is conjectured that the set of numbers $n$ that have representations $n=\sum_{u\leq i\leq v}a_i$ has positive upper density.

Combinatorics AMS 5 AMS 11

Mathematical statement

When $A =\{a_1 < \cdots\}$ corresponds to the set of primes, it is conjectured that the set of numbers $n$ that have representations $n=\sum_{u\leq i\leq v}a_i$ has positive upper density.

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_358.variants.prime_set_density_representation

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_358.variants.prime_set_density_representation :    0 < {n : ℕ | intervalRepresentations (Nat.nth Nat.Prime) n |>.Nonempty}.upperDensity := 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/358background Erdős problem 358background