| import OAI.NumberTheory.Ostmann.MainWithoutQuadraticSieve | |
| import OAI.NumberTheory.Ostmann.ZeroDensity.ComplexDensityProof | |
| namespace OAI | |
| /-! # Ostmann's inverse Goldbach theorems | |
| The quadratic large sieve and the exact character-zero density estimate give | |
| both the two-infinite-summands contradiction and asymptotic indecomposability. | |
| -/ | |
| namespace Ostmann | |
| /-- Theorem 2.3: two infinite nonnegative summands cannot give the primes | |
| outside a finite initial interval. -/ | |
| theorem twoInfiniteSummandsImpossible : TwoInfiniteSummandsImpossible := | |
| twoInfiniteSummandsImpossible_without_quadratic_sieve publishedComplexZeroDensity | |
| /-- Theorem 1.1: every sum of two nontrivial sets of nonnegative integers has | |
| infinite symmetric difference with the primes. -/ | |
| theorem inverseGoldbach : InverseGoldbach := | |
| inverseGoldbach_without_quadratic_sieve publishedComplexZeroDensity | |
| end Ostmann | |
| end OAI | |