Abstract
It is proved that lim inf n?8 (p n+1 -p n )<7×10 7 , where p n is the n -th prime. Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small gaps between consecutive primes. A major ingredient of the proof is a stronger version of the Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime divisors only, but it is adequate for our purpose
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