Large gaps between consecutive primes

Abstract
The talk is based on a joint paper by K. Ford, B. Green, S. Konyagin, and T. Tao.We prove that for any $R>0$ and sufficiently large $x$ there are $$\ge R \log x\log\log x (\log\log\log x)^{-2} \log\log\log\log x$$ consecutive composite numbers less than $x$.