Honors Theses

Date of Award


Document Type

Undergraduate Thesis



First Advisor

Tristan Denley

Relational Format



In a world of fast-paced living and information exchanging, we of the 21st century are faced with problems new and old. Among some of the new problems of our age is that of protecting our privacy in the realm of electronic information exchange. Protecting e-mail, medical records, credit card accounts, and other sensitive information is of great importance to all participants in the wired world. The business of e-security is booming as we realize the importance of protecting information as we do our tangible assets. In this aim, those in the business of securing online information call upon an area of mathematics known as prime number theory. Within this field of mathematics, we find intriguing ideas about the nature of primes as well as about how to identify and create monstrous prime numbers. The ability to construct a prime number with several hundred digits is an aim of the e-security business. Paried with generation of such numbers is the ability to classify a huge number as either prime or composite. These tasks, both aims of this paper, require the integration of concepts from as long ago as 300 B.C. and as recent as the 1990's. By studying theories, proofs, and ideas from both now and then, we can develop a solid basis for achieving both aims. From there, we can build toward understanding how we as users of this electronic world are safe and secure.

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