Asymptotically optimal packings of arithmetic progressions with prime differences

Jianfeng Hou, Siyue Liu, Hongbin Zhao

For a positive integer $n$, put $A_d=\{id:1\le i\le \lfloor n/d\rfloor \}$ for $1\le d\le n$ and $B_d=\{id:1\le i\le n\}$ for $d\in \mathbb{N}$. For $D\subseteq \{1,\dots ,n\}$, let $m…