1 \documentclass{article}
+\usepackage{amsmath}
2 \begin{document}
3
4 \section{Introduction}
5
6−This is the original version of the document.
7−We are studying the properties of prime numbers.
+This is the \textbf{revised} version of the document.
+We are studying the properties of prime numbers and their distribution.
8
9−The sum of two primes is often even.
+The sum of two odd primes is always even.
10
+\section{New Section}
+
+We added an important equation:
+\[
+ \pi(x) \sim \frac{x}{\ln x}
+\]
+
11 \section{Conclusion}
12
13−In conclusion, primes are fascinating.
+In conclusion, primes are truly fascinating objects.
14
15 \end{document}