マイク・キースの小数

$\frac{40999920000041}{999999^3}$ を小数展開すると*1、 $0$ を挟みながら $40$ 個の素数が並びます。

$\begin{align} &\quad \frac{40999920000041}{999999^3}\\ &= 0.0000\color{red}{41}0000\color{red}{43}0000\color{red}{47}0000\color{red}{53}0000\color{red}{61}0000\color{red}{71}0000\color{red}{83}0000\color{red}{97}000\color{red}{113}\\ &\quad 000\color{red}{131}000\color{red}{151}000\color{red}{173}000\color{red}{197}000\color{red}{223}000\color{red}{251}000\color{red}{281}000\color{red}{313}000\color{red}{347}00\\ &\quad 0\color{red}{383}000\color{red}{421}000\color{red}{461}000\color{red}{503}000\color{red}{547}000\color{red}{593}000\color{red}{641}000\color{red}{691}000\color{red}{743}000\color{red}{7}\\ &\quad \color{red}{97}000\color{red}{853}000\color{red}{911}000\color{red}{971}00\color{red}{1033}00\color{red}{1097}00\color{red}{1163}00\color{red}{1231}00\color{red}{1301}00\color{red}{1373}\\ &\quad 00\color{red}{1447}00\color{red}{1523}00\color{red}{1601}00\color{blue}{1681}00\color{blue}{1763}00\color{red}{1847}00\color{red}{1933}00\color{blue}{2021}00\color{red}{2111}00\\ &\quad \color{red}{2203}00\color{red}{2297}00\color{red}{2393}00\color{blue}{2491}00\color{red}{2591}00\color{red}{2693}00\color{red}{2797}00\color{red}{2903}00\color{red}{3011}00\color{red}{31} \\ &\quad \color{red}{21}00\color{blue}{3233}00\color{red}{3347}00\color{red}{3463}00\color{red}{3581}00\color{red}{3701}00\color{red}{3823}00\color{red}{3947}00\color{red}{4073}00\color{red}{4201}\\ &\quad 00\color{blue}{4331}00\color{red}{4463}00\color{red}{4597}00\color{red}{4733}00\color{red}{4871}00\color{red}{5011}00\color{red}{5153}00\color{red}{5297}00\color{red}{5443}00\\ &\quad \color{red}{5591}00\color{red}{5741}00\color{blue}{5893}00\color{red}{6047}00\color{red}{6203}00\color{red}{6361}00\color{red}{6521}00\color{blue}{6683}00\color{blue}{6847}00\color{red}{70} \\ &\quad \color{red}{13}00\color{blue}{7181}00\color{red}{7351}00\color{red}{7523}00\color{blue}{7697}00\color{red}{7873}00\color{blue}{8051}00\color{red}{8231}00\color{blue}{8413}00\color{red}{8597}\\ &\quad 00\color{red}{8783}00\color{red}{8971}00\color{red}{9161}00\color{blue}{9353}00\color{red}{9547}00\color{red}{9743}00\color{red}{9941}0\color{red}{10141}0\color{red}{10343}0\color{blue}{1}\\ &\quad \color{blue}{0547}0\color{red}{10753}0\color{blue}{10961}0\color{red}{11171}0\color{red}{11383}0\color{red}{11597}0\color{red}{11813}0\color{blue}{12031}0\color{red}{12251}0\dots\end{align}$