Guest wrote:'Bounded gaps between primes':

"It is proved that

[tex]\lim inf_{n \to \infty}(p_{n+1 } - p_{n } ) < 7 * 10^{7}[/tex],

where [tex]p_{n}[/tex] is the n-th prime.

Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small

gaps between consecutive primes. A major ingredient of the proof is a stronger version of the

Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime

divisors only (see Theorem 2 below), but it is adequate for our purpose..." -- Yitang Zhang,

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.308.998&rep=rep1&type=pdf

A Comment:

If true, that so-called celebrated result (bounded gaps between primes) of Yitang Zhang is a very weak result, and I am not impressed. And therefore, I never made the effort to review his long paper. And that Polymath project to improve on his result is also not impressive...

The twin prime conjecture and the Riemann Hypothesis give a big hint at the relevant truth.

And If one can prove the twin prime conjecture, the Riemann Hypothesis, or a weaker form of the Polignac conjecture, then that result will be a truly celebrated result.

My work on the Riemann Hypothesis and the Polignac conjecture has convinced me that they are true! And work is listed on this website too.

Dave.