- Yitang Zhang 2013 showed infinitely many prime pairs (p,q) existwith |p-q|<=70000000.Just saw lecture by Terence Tao. He says that James Maynard(who'd reduced it to 600) has joined forces with the polymath8 teamand they now have it down to 252 and expected to fall further -- heguesstimates they will stall at about 200. If the"generalized Elliott-Halberstam" conjecture is assumed they have6. Furthermore, 6 seems to be best possible, since gettingbelow 6 would require overcoming the "parity problem" obstaclepointed out by Atle Selberg, which kills all these techniques.Tao basically did not explain the techniques but did give an interestingperspective on sieve theory which was new to me.
- Hi,

Le 2014-02-27 06:53, warren.wds@... a écrit :> Yitang Zhang 2013 showed infinitely many prime pairs (p,q) exist

Cool !

> with |p-q|<=70000000.

> Just saw lecture by Terence Tao. He says that James Maynard

> (who'd reduced it to 600) has joined forces with the polymath8 team

> and they now have it down to 252 and expected to fall further -- he

> guesstimates they will stall at about 200. If the

> "generalized Elliott-Halberstam" conjecture is assumed they have

> 6. Furthermore, 6 seems to be best possible, since getting

> below 6 would require overcoming the "parity problem" obstacle

> pointed out by Atle Selberg, which kills all these techniques.

>

> Tao basically did not explain the techniques but did give an

> interesting

> perspective on sieve theory which was new to me.

do you have any publicly accessible link ?

yg