Using Repunits for Prime Factorization

This post is going to be strange! It is a nostalgia for me to think about prime numbers and prime factorization algorithms. Maybe prime numbers was the first scientific challenge of my school life, which I faced at high school. I couldn't accept the fact that there is no formula or function to find nth prime number like  Prime(n). Later I understood that most of cryptographic algorithms are based on the fact that there is no fast algorithm that is capable of factorizing large numbers consisting of just 2 big prime numbers.

I remember many days at that time, putting paper in front of me and listing lots of prime numbers to find the relation between them. After a while I found a relation between prime numbers and Repunit numbers which finally satisfied me to let the math go! and start computer science instead!! I claimed a theorem about it and also proved it.

So what are Repunit numbers?

So the theorem which I proved was this:

After 4 years, when I was graduating my B.Sc., Ayaz (my beloved master) encouraged me to write an article about it, and I did it. I was so excited to wrap it up in a paper, but unfortunately it never got out. But now, after about 10 years, I decided to publish it here in this blog.

Again, I want to thank Ayaz who made me to think about this problem and pushed me forward to write this paper.

 

You can download the full article from here.

About the author

Mehran Davoudi

A former technology geek! Currently a mentor and software architect, working as a consultant for companies with large scale software development.
Why dvd? Read about me (uɒɹɥəɯ)!

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