# Has Erdős conjecture on arithmetic progressions been proved?

The conjecture states that if $A$ is a set of natural numbers and $$\sum_{n\in A}\frac1n=\infty,$$ then $A$ contains arbitratily long arithmetic progressions.

I wonder has it been proved?

• I edited it so curious people don't need to visit wikipedia if they don't know the conjecture. Anyhow, it is a safe bet that if it had been proved, or even if a credible proof claim had been announced, the wikipedia article would have said so. – Harald Hanche-Olsen Nov 7 '12 at 8:59
• @HaraldHanche-Olsen, ok. thank you. – hxhxhx88 Nov 7 '12 at 9:00
• I've deleted my answer to this post (that the resolution of this conjecture is likely years away), as it is unhelpful. – JavaMan Nov 9 '12 at 5:07