2013 Student Research Conference:

26th Annual Student Research Conference

26th Annual Student Research Conference

**Gaussian Moat Problem**

Saru Maharjan

Prof. Tony Vazzana, Faculty Mentor

Our research is about the unsolved *Gaussian Moat Problem* which asks whether one can walk to infinity in the complex plane stepping on Gaussian primes taking steps of bounded length. A Gaussian integer is a complex number in the form of *a+bi*, where *a* and *b* are rational integers and a Gaussian prime is a Gaussian integer that cannot be decomposed into a product of two Gaussian integers in a nontrivial way. We reproduced the computational results given in the article *A Stroll Through the Gaussian Primes* by E. Gethner, S. Wagon, and B. Wick with our own codes implemented in Sage. Further, we addressed the analogous problem for Eisenstein integers and demonstrated that one cannot walk to infinity stepping on Eisenstein primes by taking steps of size √ 15 or smaller.

**Keywords:** Gaussian Moat Problem, Number Theory, Mathematics, Gaussian Integers, Gaussian Primes, Eisenstein Integers, Sage

**Topic(s):**Mathematics

**Presentation Type:** Oral Paper

**Session:** 402-2

**Location:** VH 1010

**Time:** 2:45