> [!question] Conjecture > Let $n>1$ be a positive integer. Let $k$ be the number of positive prime numbers less than or equal to $n.$ Select $k+1$ positive integers, none of which divide each other. There exists a number among the chosen $k+1$ that is bigger than $n.$ This is in fact false. For example, when $n=200,$ $k=46$ but the list (16, 6, 9, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199) of length $47$ does not contain a factor multiple pair. We can further improve this list. **Conjecture**: smallest integer so that all sets is indeed n+1 for 2n. See [[Given a set of 𝑛+1 numbers out of the first 2𝑛 natural numbers, {1,2,…,2𝑛}, there are two numbers in the set, one of which divides the other]].