Date of Award
6-2016
Document Type
Open Access
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Kathryn Lesh
Language
English
Keywords
prime, suppose, cubic, rational, proposistion, primality
Abstract
According to the Berrizbeitia theorem, a highly efficient method for certifying the primality of an integer N ≡ 1 (mod 3) can be created based on pseudocubes in the ordinary integers Z. In 2010, Williams and Wooding moved this method into the Eisenstein integers Z[ω] and defined a new term, Eisenstein pseudocubes. By using a precomputed table of Eisenstein pseudocubes, they created a new algorithm in this context to prove primality of integers N ≡ 1 (mod 3) in a shorter period of time. We will look at the Eisenstein pseudocubes and analyze how this new algorithm works with the Berrizbeitia theorem.
Recommended Citation
Jia, Miaoqing, "Primality Proving Based on Eisenstein Integers" (2016). Honors Theses. 162.
https://digitalworks.union.edu/theses/162
Included in
Applied Mathematics Commons, Logic and Foundations of Mathematics Commons, Mathematics Commons