I have an interval $[2,t]$ containing some number of primes. I now want to divide this interval into two intervals $a=[2,m]$ and $b=]m,t]$ such that the number of primes in $a$ and $b$ is almost the same.
I am aware of the approximation $\pi(t)=\frac{t}{2\ln(t)}$, but can not seem to get any good and usable result out of this.
This is for a computer implementation, so avoiding Lambert functions and likewise functions would be much appreciated.