Ostmann's inverse Goldbach conjecture

Theorem 1.1: if $A,B\subseteq\mathbb N_0$ have $|A|,|B|\ge2$, then $(A+B)\triangle\mathcal P$ is infinite. After the Laffer-Mann reduction to two infinite summands, the proof combines residue restrictions at every prime, decorrelation from translated multiplicative characters, prime coverage and a positive statistic averaged over arrangements; it does not use Green and Harper's conditional inverse-sieve route. In particular, if $A+B$ contains every large prime it contains infinitely many composites. No quantitative version is claimed.

Theorem 1.1: if $A,B\subseteq\mathbb N_0$ have $|A|,|B|\ge2$, then $(A+B)\triangle\mathcal P$ is infinite. After the Laffer-Mann reduction to two infinite summands, the proof combines residue restrictions at every prime, decorrelation from translated multiplicative characters, prime coverage and a positive statistic averaged over arrangements; it does not use Green and Harper's conditional inverse-sieve route. In particular, if $A+B$ contains every large prime it contains infinitely many composites. No quantitative version is claimed.