As a final year student I'm required to do one project in mathematics, which is what I have always wanted to do! To make it more interesting, I have decided to write about this project here as a blog post.
The topic for my project is "computational number theory ", more specifically on primality tests and integer factorization algorithms.
Why I chose this topic?
I have interests in both mathematics and computer science and I had this in mind for some time to do some concrete work in both the fields. Also nowadays I'm studying algorithms, so I thought it a good idea to choose my project related to algorithms.
In my first year in college I read a book on number theory:
Elementary Number Theory by David Burton
It's an amazing book, especially the part of the theory of congruence, Chinese remainder theorem and continued fractions. I had developed some interest in number theory after reading that book.
So when it comes to project, honestly I couldn't think of anything else but Number Theory in which i already have good knowledge and experience.
Exactly what my project is about?
Prime numbers and Primality tests and Integer Factorization, which is one of the most important topics in number theory, will be the main focus of my project. The subject of primality of a number has been the focus of many scientific studies and several different theories has been developed for many years. Based on these theorems, primality of large numbers has been investigated. There are also computer algorithms to test primality of large numbers. I will be discussing different methods, algorithms to check primality and to factor large integers. I will also discuss about the best and worst cases for such algorithms, try to compare them and explain which algorithm is best in what condition. The Best method/algorithm will determined by comparing the test results with different methods/algorithms.
Apart from primality and Integer Factorization I will be giving an Introduction to some of the named primes such as Mersenne primes, Gaussian primes, irregular primes etc.
