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The Quarterly Journal of Mathematics Advance Access published online on October 29, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han026
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

A NOTE ON THE SUM OF THE FIRST n PRIMES

Kaisa Matomäki{dagger}

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

{dagger} Address for correspondence: Department of Mathematics, 20014 University of Turku, Finland; E-mail address: ksmato{at}utu.fi

Received 7 March 2008; revised 17 July 2008
  Abstract

We show that the arithmetic mean of the first n primes is an integer for<<N19/24+{epsilon} numbers n≤N. This follows from showing that the discrepancy of the sequence consisting of the arithmetic means is<<N–5/24+{epsilon}.


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