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bound in base 10
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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)$$x<\exp(727.951332668)<1.4\cdot 10^{316}$ for which $\theta(x)>x$.

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 $x<\exp(727.951332668)$ for which $\theta(x)>x$.

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 $\theta(x)>x$.

Source Link
Stopple
  • 11.1k
  • 3
  • 43
  • 65

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 $x<\exp(727.951332668)$ for which $\theta(x)>x$.