Erdős conjectured, in over a dozen papers spanning 1976 to 1997 and with a 1000 dollars prize attached, that every finite Sidon set extends to a perfect difference set modulo $p^2+p+1$ for some prime $p$. Alexeev and Mixon establish that $\{1,2,4,8\}$ is a counterexample - and discovered along the way that Marshall Hall, Jr. had published a different counterexample three decades before Erdős first posed the problem, unnoticed by the community for half a century.