SOLVED
Suppose $A\subseteq \{1,\ldots,N\}$ is such that there are no $k+1$ elements of $A$ which are relatively prime. An example is the set of all multiples of the first $k$ primes. Is this the largest such set?
This was disproved for $k=212$ by Ahlswede and Khachatrian
[AhKh94], who suggest that their methods can disprove this for arbitrarily large $k$.
Erdős later asked ([Er92b] and [Er95]) if the conjecture remains true provided $N\geq (1+o(1))p_k^2$ (or, in a weaker form, whether it is true for $N$ sufficiently large depending on $k$).
See also [534].
