Theorems · Theorem · number theory
not_summable_one_div_on_primes
- #81 of the 100 theorems: Divergence of the Prime Reciprocal Series
¬Summable ({p | Nat.Prime p}.indicator fun n => 1 / ↑n)The sum over the reciprocals of the primes diverges.
- Defined in
- Mathlib.NumberTheory.SumPrimeReciprocals
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Set.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Finset.sumproof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement and proof · cited by 2,059
Cited by2
Results whose statement or proof uses this declaration.
- ArithmeticFunction.not_LSeriesSummable_moebius_at_oneproof · cited by 1
- Nat.Primes.not_summable_one_divproof · cited by 1