Erdős Problem 687

### What is the conjecture

https://www.erdosproblems.com/687

Let $Y(x)$ be the maximal $y$ such that there exists a choice of congruence classes $a_p$ for all primes $p\leq x$ such that every integer in $[1,y]$ is congruent to at least one of the $a_p\pmod{p}$.

Give good estimates for $Y(x)$. In particular, can one prove that $Y(x)=o(x^2)$ or even $Y(x)\ll x^{1+o(1)}$?

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 by reading the linked Erdős Problems entry for Problem 687 and reviewing how this repository formalizes existing conjectures. No target file or test is named; done means adding a formal statement of the conjecture to the collection with the repository's expected validation passing.

Written by the indexing model from the issue text.