English
If 2^p − 1 is prime, then p is prime.
Русский
Если 2^p − 1 простое, то p простое.
LaTeX
$$$$\text{If } \mathrm{mersenne}(p) \text{ is prime, then } p \text{ is prime}.$$$$
Lean4
instance : Finite 𝓀[K] :=
letI := IsTopologicalAddGroup.toUniformSpace K
haveI := isUniformAddGroup_of_addCommGroup (G := K)
letI : (Valued.v (R := K)).RankOne := ⟨IsRankLeOne.nonempty.some.emb, IsRankLeOne.nonempty.some.strictMono⟩
(compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField.mp
(inferInstanceAs (CompactSpace 𝒪[K]))).2.2
