Small gaps between primes and primes in arithmetic progressions to large moduli

Let p(n) denote the n-th prime. We describe the proof of the recent result lim inf(n -> 8) (p(n+1) - p(n)) < infinity, which is closely related to the distribution of primes in arithmetic progressions to large moduli. A major ingredient of the argument is a stronger version of the Bombieri-Vinogradov theorem which is applicable when the moduli are free from large prime factors.