Abstract. Let An be the (unweighted) arithmetic mean of the first n prime numbers. We prove that for n ≥ 2,
A<sub>n</sub><sup>1+α/(n*log(n))</sup> ≤ A<sub>n+1</sub> ≤ A<sub>n</sub><sup>1+β/(n*log(n))</sup>
with the best possible constants α ≈ 0.43525 and β ≈ 1.22596. The right-hand side improves a result given by Z.-W. Sun in 2013.
