ar X iv : 0 71 0 . 27 28 v 1 [ m at h . N T ] 1 5 O ct 2 00 7 PRIMES IN TUPLES II
نویسنده
چکیده
We prove that lim inf n→∞ pn+1 − pn √ log pn(log log pn) < ∞, where pn denotes the n prime. Since on average pn+1 −pn is asymptotically log pn, this shows that we can always find pairs of primes much closer together than the average. We actually prove a more general result concerning the set of values taken on by the differences p− p between primes which includes the small gap result above.
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تاریخ انتشار 2007