Problem Statement
A set $A\subset \mathbb{N}$ is primitive if no member of $A$ divides another. Is the sum\[\sum_{n\in A}\frac{1}{n\log n}\]maximised over all primitive sets when $A$ is the set of primes?
Categories:
Number Theory Primitive Sets
Progress
Erdős [Er35] proved that this sum always converges for a primitive set. Lichtman [Li23] proved that the answer is yes.Source: erdosproblems.com/164 | Last verified: January 13, 2026