The Erdős conjecture on arithmetic progressions states that if A is a subset of the natural numbers such that the sum of reciprocals of its elements diverges, then A contains arithmetic progressions of every length.

When A is taken to be the set of primes, this is the Green-Tao theorem. The conjecture is also proven for the special case of 3-element arithmetic progressions.

https://www.erdosproblems.com/3

The close date of this market will be extended until such time as the conjecture is resolved one way or the other.