Erdős Problem 1113
Erdős Problem 1113.* Do there exist Sierpiński numbers that possess no finite covering set of primes?
Mathematical statement
Erdős Problem 1113.* Do there exist Sierpiński numbers that possess no finite covering set of primes?
Erdős and Graham [ErGr80] conjectured that the answer is yes. A negative answer would imply that there are infinitely many Fermat primes.
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_1113
theorem erdos_1113 : answer(sorry) ↔ ∃ k, k.IsSierpinskiNumber ∧ ¬ HasFinitePrimeCoveringSet k := 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