Is there an elementary argument for proving $$\forall x \ge 17:\pi(x)>\dfrac x{\ln x} $$ ? where $\pi(x)$ is the prime counting function ....
2026-04-12 09:32:39.1775986359
To prove $\pi(x)>\dfrac x{\ln x} , \forall x \ge 17$ by elementary argument
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I doubt that it's "elementary", but according to Wikipedia e.g. Dusart proves $$ \pi(x) > \dfrac{x}{\ln x} + \dfrac{x}{\ln(x)^2} \ \text{for} x \ge 599 $$ and then you can check it for each integer $x \in [17, 598]$.