Erdős Problem 432

### What is the conjecture

https://www.erdosproblems.com/432

Let $A,B\subseteq \mathbb{N}$ be two infinite sets. How dense can $A+B$ be if all elements of $A+B$ are pairwise relatively prime?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start with the conjecture statement and the linked Erdős Problems page, then inspect existing formalized conjectures in the repository to find the relevant structure and conventions. Done means adding a Lean formalization of Problem 432 that matches the repository's established pattern.

Written by the indexing model from the issue text.