Logic and Foundations of Mathematics Commons^™

Primality Proving Based On Eisenstein Integers, Miaoqing Jia

Honors Theses

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 …