# What is the narrowest interval I=[a,b] such that there are infinitely prime gaps of size in I?

Polymath8b project allowed, building on Zhang's 2013 breakthrough, to prove that there are infinitely prime gaps of size less or equal to 600. Under the generalized Elliott-Halberstam conjecture, one can reach the upper bound 6.

My question is: in early August 2016, what is the narrowest interval $I=[a,b]$ such that we know that there are infinitely many prime gaps whose size belongs to $I$?

I'm essentially interested in unconditional results, but those obtained under very plausible conjectures such as (G)EH and or (G)RH can be of some interest too.