Bounded gaps between primes
نویسنده
چکیده
It is proved that lim inf n→∞ (pn+1 − pn) < 7× 10, where pn 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.
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