My personal projects offer a window into my passions and interests, showcasing the work I’ve pursued over the years. AI and mathematics have always been constants in my journey, fueling my curiosity and driving many of these endeavors. Personally and professionally, I have worked with a broad range of technologies, gaining diverse skills.
Integer Factorization: Pushing the Boundaries of Computational Efficiency
Integer factorization has been an ongoing passion of mine, and I’ve dedicated significant time and effort toward developing an efficient algorithm for factoring large integers. My goal has always been to achieve logarithmic time complexity, a challenge that continues to drive my work in computational number theory.
A while back, I created an algorithm that performed well in factorizing integers, and I'm proud to share the source code with the community. You can explore it on my GitHub repository.
The algorithm centers around creating and solving a series of binary equations. It's a clever approach, but I believe there's room for improvement, particularly through the application of advanced techniques like Binary Decision Diagrams (BDD) and p-adic numbers. These methods could offer more efficient ways to represent and solve the factorization problem, pushing the boundaries of what's currently achievable.
I've been greatly inspired by Donald Knuth's work in this area, especially his insightful books. I plan to continue refining my approach in the future and incorporate these advanced methods to further optimize the algorithm.
I've been greatly inspired by Donald Knuth's work in this area, especially his insightful books. I plan to continue refining my approach in the future and incorporate these advanced methods to further optimize the algorithm. Feel free to explore the code, and I welcome any feedback or collaboration from fellow enthusiasts in the field.
Technologies: PHP
