Ostmann’s inverse Goldbach conjecture

Proves that no finite modification of the primes can be written as A+B with A,B\subseteq\mathbb Z_{\ge0} each containing at least two elements. This resolves Ostmann's inverse Goldbach conjecture on additive indecomposability. (Lean)

Manuscript

The additive indecomposability of the primes

September 24, 2026 · source · cite as \cite{OAI:the-additive-indecomposability-of-the-primes-September-24-2026}

We prove Ostmann's inverse Goldbach conjecture: no set differing from the primes by finitely many elements can be written as A+B, where A and B are sets of nonnegative integers with at least two elements each.

Result 013 · Number theory. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.