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\section{Introduction}  This is a hand-in written by \textbf{Group 7} (FIRE) for the Algorithms course (TIN092) at Chalmers University of Technology.  Group 7 consists of:   \begin{itemize}  \item \textbf{Mazdak Farrokhzad}  \begin{itemize}  \item 901011-0279  \item [email protected]  \item Program: IT  \end{itemize}  \item \textbf{Niclas Alexandersson}  \begin{itemize}  \item 920203-0111  \item [email protected]  \item Program: IT  \end{itemize}  \end{itemize}  This hand in deals with complexity analysis of an algorithm $prime(n)$  The algorithm is as follows: