This report explores the historical development of three areas of study regarding prime numbers. The attempt to find an efficient and useful function to generate primes could be a helpful tool in the improvement of encryption. The difficulty of factoring large numbers allows the Rivest, Shamir and Adleman algorithm to be effective for public key cryptography. The distribution of primes is examined through discussion of the prime number theorem and the Riemann hypothesis. A brief case for integrating elementary number theory in secondary curriculum is also included. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

In this dissertation we show that the Giulietti-Ughi arc is not complete for large primes. This arc is complete for primes which are congruent to three modulo four and less than thirty one. The cardinality of this arc has the same order as the Lunelli-Sce bound. We use two powerful theorems, one on the classifications of Galois groups of quintic polynomials and the other, the Čebotarev density theorem for function fields to show that there exist points on a certain curve which are not covered by the arc. We then outline a technique which could be used to extend the arc to a complete arc.

No description available.

[Please see thesis for abstract.] / vi, 114 leaves ; 29 cm

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1951. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 582-591).

P. Laborde Montaner's Thesis--New York University, 1951. / Includes bibliographical references (p. 43).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 100-104).

Thesis (Ph.D.)--University of California, 1909. / Vita.