How to display chapter number in big numerical next to chapter title

Here is a solution, with two (not Fifty) Shades of Grey:

\documentclass[10pt,twoside]{book}
\usepackage[utf8]{inputenc}
\usepackage{lipsum, graphicx, tabularx}
\usepackage[svgnames]{xcolor}
\usepackage[explicit]{titlesec}
% todo modify this to display chapter name and number as shown in figure above.
\titleformat{\chapter}[block]
    {\bfseries\Huge\sffamily}
    {\rlap{\hspace*{\dimexpr\linewidth+\marginparsep}%
\parbox{\marginparwidth}{\centering\color{Gainsboro}\scalebox{4}{\thechapter}\\[-0.5ex]% \raisebox{-0.3\height}[0pt][0pt]
    \rule{10pt}{10pt}\hspace{10pt}\rule{10pt}{10pt}\hspace{10pt}\rule{10pt}{10pt}}}}
    {0pt}
    {\color{gray!75}\begin{tabularx}{\linewidth}{@{}>{\raggedright\arraybackslash}X>{\raggedleft\arraybackslash}p{1cm}@{}}
       & \makebox[0pt]{\LARGE\chaptername}\\[2.5ex] #1
    \end{tabularx}}
    [\vspace{1ex}\titlerule\vspace{16pt}]

\titlespacing{\chapter}{0pt}{-5ex}{10ex}

\usepackage{currfile}
\usepackage{lipsum}

\usepackage{shorttoc}
\usepackage{tocbibind}
% http://ctan.org/pkg/bookmark
\usepackage{bookmark}
\usepackage{listings}
\usepackage{wrapfig}

\usepackage{float}

\begin{document}

\chapter{Random Number Generators}

\lipsum[1-5]

\end{document}

For problems with the margin, I propose this variant:

\documentclass[10pt,twoside]{book}
\usepackage[utf8]{inputenc}% Page dimensions required by publisher
\usepackage[paperwidth=16.99cm,paperheight=24.4cm,]{geometry} % showframe
\usepackage{lipsum, graphicx, tabularx}
\usepackage[svgnames]{xcolor}
\usepackage[explicit]{titlesec}
% todo modify this to display chapter name and number as shown in figure above.
\titleformat{\chapter}[block]
    {\bfseries\Huge\sffamily}
    {\rlap{\hspace*{\dimexpr\linewidth+2 \marginparsep}%
    \begin{tabular}{@{}>{\color{Gainsboro}}c@{}}\scalebox{4}{\thechapter}\\[-0.5ex]%
    \rule{10pt}{10pt}\hspace{10pt}\rule{10pt}{10pt}\hspace{10pt}\rule{10pt}{10pt}\end{tabular}}}
    {0pt}
    {\color{gray!75}\begin{tabularx}{\dimexpr\linewidth+4\marginparsep}%
    {@{}>{\raggedright\arraybackslash}X>{\raggedleft\arraybackslash}r@{}}
       & \rule{0pt}{3ex}\LARGE\chaptername\\[0ex] #1
    \end{tabularx}}
    [\vspace{1ex}\titlerule\vspace{16pt}]

\titlespacing{\chapter}{0pt}{-5ex}{10ex}

\usepackage{currfile}
\usepackage{lipsum}

\usepackage{shorttoc}
\usepackage{tocbibind}
% http://ctan.org/pkg/bookmark
\usepackage{bookmark}
\usepackage{listings}
\usepackage{wrapfig}

\usepackage{float}

\begin{document}

\chapter{Random Number Generators}

\lipsum[1-5]
\end{document} 

An example using the memoir class, lightly modified from Various chapter styles for the memoir class:

\documentclass{memoir}
\usepackage{lipsum}
\usepackage{xcolor}
\newif\ifchapternonum
\makechapterstyle{jenor}{
\renewcommand\printchaptername{}
\renewcommand\printchapternum{}
\renewcommand\printchapternonum{\chapternonumtrue}
\renewcommand\chaptitlefont{\sffamily\bfseries%
\fontsize{25}{35}\selectfont\raggedright}
\renewcommand\chapnumfont{\fontfamily{pbk}\fontseries{m}\fontshape{n}%
\fontsize{2in}{0in}\selectfont\color{gray!50}}
\renewcommand\printchaptertitle[1]{%
\ifchapternonum%
\begin{tabularx}{\textwidth}{X}%
{\parbox[b]{\linewidth}{\chaptitlefont ##1}%
\vphantom{\raisebox{-15pt}{\chapnumfont 1}}}
\end{tabularx}%
\else
\begin{tabularx}{\textwidth}{Xl}
{\parbox[b]{\linewidth}{\chaptitlefont ##1}}
& \raisebox{-15pt}{\chapnumfont \thechapter}%
\end{tabularx}%
\fi
\par\vskip2mm\hrule
}}

\chapterstyle{jenor}

\begin{document}
\chapter{Random Number Generators}
\section*{Introductiom}
\lipsum[1]
\end{document}