Date of Award

2006

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Andrew H. Knightly

Second Committee Member

Henrik Bresinsky

Third Committee Member

Ali E. Özlük

Abstract

In August of 2002, three Indian computer scientists, Manindra Agrawal, Neeraj Kayal arid Nitin Saxena, released a paper simply titled 'PRMlES is in P'. Within a scant number of pages, they were able to clearly demonstrate a deterministic polynomial time primality test,. Surprisingly enough, the direction they took had long since been passed over by nearly all other mathematicians as a dead end. By pushing further ahead using commonly known facts about the prime numbers, they created an algorithm that is not only elegant in its proof, but also one that can be adapted to run on multiple processors with nearly perfect speedup. This thesis will explore the characterization of prime numbers presented by the three scientists. It will also provide a parallel implementation of the algorithm using freely available tools. The discussion of the implementation will include complexity calculations, numerous examples of real-life runtimes for various integers, calculations of speedup and optimal number of processors, as well as key portions that are ripe for improvement.

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