Yitang Zhang: Prime Gaps

Question

Has anybody read Yitang Zhang's paper on prime gaps? Wired reports "$70$ million" at most, but I was wondering if the number was actually more specific.

*EDIT*$^1$:

Are there any experts here who can explain the proof? Is the outline in the annals the preprint or the full accepted paper?

Answer 1

70 million is exactly what is mentioned in the abstract.

It is quite likely that this bound can be reduced; the author says so in the paper:

This result is, of course, not optimal. The condition $k_0 \ge 3.5 \times 10^6$ is also crude and there are certain ways to relax it. To replace the right side of (1.5) by a value as small as possible is an open problem that will not be discussed in this paper.

He seems to be holding his cards for the moment...

You can download a copy of the full accepted paper on the Annals page if your institution subscribes to the Annals.

Answer 2

As to the "idea" of the proof, I would suggest looking at the following.

As mentioned by Mark Lewko, according to WolframAlpha, the proof gives a gap size of $63, 374, 610.$