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Variants of the Selberg sieve, and bounded intervals containing many primes

Abstract:

For any m≥1, let H m denote the quantity MathML. A celebrated recent result of Zhang showed the finiteness of H1, with the explicit bound H1≤70,000,000. This was then improved by us (the Polymath8 project) to H1≤4680, and then by Maynard to H1≤600, who also established for the first time a finiteness result for H m for m≥2, and specifically that H m ≪m3e4m. If one also assumes the Elliott-Halberstam conjecture, Maynard obtained the bound H1≤12, improving upon the previous bound H1≤16 of Gold...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1186/s40687-014-0012-7

Authors


Contributors

Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Contributor
Publisher:
Springer International Publishing
Journal:
Research in the Mathematical Sciences More from this journal
Volume:
1
Issue:
12
Pages:
83
Publication date:
2014-10-17
DOI:
ISSN:
2197-9847
Keywords:
Pubs id:
pubs:653371
UUID:
uuid:fd360b0e-b594-41fa-9fff-6d8adbd07ef9
Local pid:
pubs:653371
Deposit date:
2016-10-21

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