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Bounded gaps between primes
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DOI：10.4007/annals.2014.179.3.7.png)
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Abstract
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It is proved that lim inf(n ->infinity)(p(n+1)-p(n)) < 7 x 10(7), where p(n) is the n-th prime. Our method is a refinement of the recent work of Goldston, PintzandY1ld1rm 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.
Keywords:
ARITHMETIC PROGRESSIONS
LARGE MODULI
NUMBERS
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