Improving Zhang's prime gap

Question

I am referring to Zhang's paper.

Since the set $\cal{H}$ is a subset of $[3.5\times 10^6, 7\times 10^7]$, shouldn't the prime gap he obtained be less than $ 7\times 10^7 - 3.5\times 10^6$ rather than $7\times 10^7$, as stated in his paper? Or am I missing something here?

Answer 1

Indeed, the gap size can be brought down to below 60 million (in particular, to 59,874,594) by more careful choice of parameters, according to a short preprint by Timothy Trudgian.

Edit: Further work has reduced the bound to 13,008,612.

Edit: Following Maynard's work and the subsequent improvements of the Polymath project, the bound has been lowered to 246: Variants of the Selberg sieve, and bounded intervals containing many primes