We create an array of points $P_n$ in a two dimensional plane using the following random number generator:
$s_0=290797$
$s_{n+1}={s_n}^2 \bmod 50515093$

$P_n=(s_{2n},s_{2n+1})$

Let $d(k)$ be the shortest distance of any two (distinct) points among $P_0, \cdots, P_{k - 1}$.
E.g. $d(14)=546446.466846479$.

Find $d(2000000)$. Give your answer rounded to $9$ places after the decimal point.