Platt and Trudgian show in http://arxiv.org/abs/1407.1914 that $$ \theta(x)<x\quad\text{for}\quad x<1.39\cdot 10^{17} $$ and there is an $x<\exp(727.951332668)<1.4\cdot 10^{316}$ for which $\theta(x)>x$.
Stopple
- 11.1k
- 3
- 43
- 65