Yitang Zhang made a groundbreaking discovery when he proved that there are infinitely many pairs of prime numbers which differ by less than $70,000,000$.
Zhang's theorem has been significantly improved and, according to the Polymath8 project home page (http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes), the best unconditional bound to date is $246$.
Suppose the bound is lowered enough so as to prove the twin prime conjecture. If this happens, then one of the most famous unsolved problems in Mathematics will have been solved. But what will happen with Polignac's conjecture?
Polignac's conjecture states that for every positive integer $n$ there are infinitely many pairs of prime numbers whose difference is $2n$. So, since the twin prime conjecture is just a particular case of Polignac's conjecture, proving the former does not imply that the latter is true.
I know that probably now many mathematicians are trying to lower the bound enough so as to prove the twin prime conjecture. But, is any progress being made towards the solution of Polignac's conjecture? Can Zhang's discovery and his techniques be used in any way to make progress towards the solution of Polignac's conjecture, or should another groundbreaking discovery be made? Is now Polignac's conjecture closer to be proved or is it still "out of reach"?