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The Quarterly Journal of Mathematics Advance Access published online on August 10, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham021
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Large differences between consecutive primes

Kaisa Matomäki{dagger}

Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

{dagger} E-mail: k.s.matomaki{at}rhul.ac.uk

Received 25 August 2006; revised 20 February 2007
  Abstract

We use a sieve method together with mean and large value results for Dirichlet polynomials to prove that

Formula
where pn is the nth prime number.


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