Sierpiński number
The Sierpiński problem (Selfridge's conjecture).* Is 78557 the smallest Sierpiński number?
Mathematical statement
The Sierpiński problem (Selfridge's conjecture).* Is 78557 the smallest Sierpiński number?
Selfridge conjectured that 78557 is the smallest Sierpiński number. He proved in 1962 that 78557 is indeed a Sierpiński number by showing that all numbers of the form have a factor in the covering set .
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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
selfridge_conjecture
theorem selfridge_conjecture : answer(sorry) ↔ IsLeast {k | k.IsSierpinskiNumber} 78557 := 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