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On limit points of the sequence of normalized prime gaps

Abstract:
Let pnpn denote the nnth smallest prime number, and let LL denote the set of limit points of the sequence {(pn+1−pn)/logpn}∞n=1{(pn+1−pn)/log⁡pn}n=1∞ of normalized differences between consecutive primes. We show that, for any sequence of nine nonnegative real numbers β1≤β2≤⋯≤β9β1≤β2≤⋯≤β9, at least one of the numbers βj−βiβj−βi (1≤i
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1112/plms/pdw036

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Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Oxford University Press Publisher's website
Journal:
Proceedings of the London Mathematical Society Journal website
Volume:
113
Issue:
4
Pages:
515-539
Publication date:
2016-08-23
Acceptance date:
2016-08-23
DOI:
EISSN:
1460-244X
ISSN:
0024-6115
Pubs id:
pubs:653368
URN:
uri:aa4199bb-d60f-4da4-875e-7f84b6099d32
UUID:
uuid:aa4199bb-d60f-4da4-875e-7f84b6099d32
Local pid:
pubs:653368
Paper number:
4
Keywords:

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