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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 $x$.