In August 2002, three Indian researchers, Manindra Agrawal and his students Neeraj Kayal and Nitin Saxena at the Indian Institute of Technology in Kanpur, presented a remarkable algorithm (the AKS algorithm) in their paper "PRIMES is in P." It is a deterministic polynomial-time algorithm that determines whether an input number is prime or composite. No such algorithm was known so far and it has fundamental meaning for complexity theory. This project is centered around the AKS algorithm from the "PRIMES is in P" paper. The objectives are both experiments with the AKS algorithm and theorems and lemmas showing the correctness of the algorithm. One of the tasks of the project is to provide easy-to-follow explanations of the original paper for average mathematically mature readers. We also analyze the AKS algorithm in detail. Ideas and concepts in the algorithm are studied and possibilities of improvements of the algorithm are explored.

Publication Date


Document Type

Master's Project

Student Type


Department, Program, or Center

Computer Science (GCCIS)


Radziszowski, Stainslaw - Chair

Advisor/Committee Member

Hemaspaandra, Edith

Advisor/Committee Member

Anderson, Peter


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