Book section
Chains of large gaps between primes
- Abstract:
- Let pn denote the n-th prime, and for any k > 1 and sufficiently large X , define the quantity Gk (X ) := max/pn+k≼X min(pn+1 − pn,..., pn+k − pn+k−1), which measures the occurrence of chains of k consecutive large gaps of primes. Recently, with Green and Konyagin, the authors showed that G1(X) ≫ log X log log X log log log log X/log log log X for sufficiently large X . In this note, we combine the arguments in that paper with the Maier matrix method to show that Gk (X ) ≫ 1/k^2 log X log log X log log log log X/log log log X for any fixed k and sufficiently large X . The implied constant is effective and independent of k.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Accepted manuscript, pdf, 162.8KB, Terms of use)
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- Publisher copy:
- 10.1007/978-3-319-92777-0_1
- Publisher:
- Springer
- Host title:
- Irregularities in the Distribution of Prime Numbers: From the Era of Helmut Maier's Matrix Method and Beyond
- Pages:
- 1-21
- Chapter number:
- 1
- Publication date:
- 2018-07-05
- Acceptance date:
- 2016-12-01
- DOI:
- ISBN:
- 9783319927763
- Language:
-
English
- Keywords:
- Pubs id:
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pubs:666840
- UUID:
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uuid:2ba965da-7ce1-418e-96aa-5f119f965910
- Local pid:
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pubs:666840
- Deposit date:
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2016-12-21
Terms of use
- Copyright holder:
- Springer
- Copyright date:
- 2018
- Rights statement:
- © Springer International Publishing AG, part of Springer Nature 2018.
- Notes:
- This is the accepted manuscript version of the chapter. The final version is available online from Springer at: http://dx.doi.org/10.1007/978-3-319-92777-0_1
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