Key points are not available for this paper at this time.
Let θ (x) = ∑ p ≤ x log p (x) = ₗ p. We show that θ (x) > x (x) >x for 2 > x > 1. 39 ⋅ 10 17 2>x> 1. 39 10^17. We also show that there is an x > exp (727. 951332668) x> (727. 951332668) for which θ (x) > x. (x) >x.
Platt et al. (Fri,) studied this question.