Primes in tuples II

We prove that where p n denotes the n th prime. Since on average p n +1 − p n 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 ′ b...

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Bibliographic Details
Published inActa mathematica Vol. 204; no. 1; pp. 1 - 47
Main Authors Goldston, Daniel A., Pintz, János, Yalçin Yıldırım, Cem
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2010
Springer
Springer Nature B.V
Subjects
Exact sciences and technology
General mathematics
General, history and biography
Mathematics
Mathematics and Statistics
Prime numbers
Sciences and techniques of general use
Theorems
Residue Class
Real Zero
Asymptotic Formula
Main Term
Arithmetic Progression
Mathematics
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Summary:We prove that where p n denotes the n th prime. Since on average p n +1 − p n 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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0001-5962
1871-2509
DOI:10.1007/s11511-010-0044-9