Erdős conjecture on arithmetic progressions

Statement

Every large set of natural numbers, i.e., every subset of the set of natural numbers whose sum of reciprocals diverges, contains aribtrarily long arithmetic progressions.

Relation with other facts/conjectures

Weaker facts

Name	Statement	Proof of implication
Green-Tao theorem	This states that the set of primes contains arbitrarily long arithmetic progressions	set of primes is large