As it is stated, for instance, in Wikipedia, the Riemann hypothesis is equivalent to $$ |\pi(x)-{\rm li}(x)|< \frac1{8\pi}\sqrt x\log x,\qquad \mbox{for all } x\geq 2\,657, $$ but "li" denotes there the complete logarithmic integral: $$ {\rm li}(x)=\int_0^x\frac{dt}{\log t}. $$
I have checked with Mathematica that the inequality fails for $x=2\,656$. However, what happens if the offset logarithmic integral $$ {\rm Li}(x)=\int_2^x\frac{dt}{\log t} $$ is considered instead?
I have checked that, in the range $1\leq x\leq 100\,000$, the corresponding inequality holds for $x\geq 1\,447$.
Is the Riemann hypothesis equivalent to $$ |\pi(x)-{\rm Li}(x)|< \frac1{8\pi}\sqrt x\log x,\qquad \mbox{for all } x\geq 1\,447\ ? $$ All the references I have found deal with li instead of Li.