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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 785572n+178557 \cdot 2^n + 1 have a factor in the covering set {3,5,7,13,19,37,73}\{3, 5, 7, 13, 19, 37, 73\}.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

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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

Canonical source
Complete statement target, proof intentionally absentLean 4
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