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- W2097249100 abstract "We prove that $ mathop{ lim inf}limits_{n rightarrow infty} frac{p_{n+1}-p_{n}}{sqrt{log p_{n}} left(log log p_{n}right)^{2}}< infty, $where pn denotes the nth prime. Since on average pn+1−pn is asymptotically log n, 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." @default.
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- W2097249100 date "2010-01-01" @default.
- W2097249100 modified "2023-10-17" @default.
- W2097249100 title "Primes in tuples II" @default.
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- W2097249100 doi "https://doi.org/10.1007/s11511-010-0044-9" @default.
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