Tianhan Dai

Note on a conjecture of Ram\'ırez Alfons\'ın and Skałba

Let $2< a<b$ be two relatively prime integers and $g=ab-a-b$. It is proved that there exists at least one prime $p\le g$ of the form $p=ax+by~(x,y\in \mathbb{Z}_{\ge 0})$, which confirms a 2020 conjecture of Ram\'ırez Alfons\'ın and Skałba.