A NOTE ON THE SUM OF THE FIRST n PRIMES

: Matomäki Kaisa

Publisher: OXFORD UNIV PRESS

: 2010

: Quarterly Journal of Mathematics

: QUARTERLY JOURNAL OF MATHEMATICS

: Q J MATH

: 1

: 61

: 1

: 109

: 115

: 7

: 0033-5606

DOI: https://doi.org/10.1093/qmath/han026

We show that the arithmetic mean of the first n primes is an integer for < N(19/24+epsilon) numbers n < N. This follows from showing that the discrepancy of the sequence consisting of the arithmetic means is < N(-5/24+epsilon).