There are some integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. One of them is the integral introduced by Selberg related to estimating the variance of primes in short intervals: I read the last interesting paper of Yitang Zhang and it seems to me that the paper discusses the statistical distribution of Landau-Siegel zeros and primes as well. In the same time the correlation conjecture of H. L. Montgomery deals with estimation of the variance of primes.

My Question is: assuming Yitang Zhang latest results correct, to what extent these results would contribute to correlation conjecture of H. L. Montgomery?

Note: I ask kindly community to add tag for Yitang Zhang results or Yitang Zhang theorem.