Date of Award
Bachelor of Science
prime, suppose, cubic, rational, proposistion, primality
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.
Jia, Miaoqing, "Primality Proving Based on Eisenstein Integers" (2016). Honors Theses and Student Projects. 162.