Bounded gaps between primes

Bounded gaps between primes

'Bounded gaps between primes':

"It is proved that

$$\lim inf_{n \to \infty}(p_{n+1 } - p_{n } ) < 7 * 10^{7}$$,

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 (see Theorem 2 below), but it is adequate for our purpose..." -- Yitang Zhang,