## Experimental Mathematics

- Experiment. Math.
- Volume 10, Issue 2 (2001), 161-174.

### The Gaussian Zoo

John Renze, Stan Wagon, and Brian Wick

#### Abstract

We find all the maximal admissible connected sets of Gaussian primes: there are 52 of them. Our catalog corrects some errors in the literature. We also describe a totally automated procedure to determine the heuristic estimates for how often various patterns, in either the integers or Gaussian integers, occur in the primes. This heuristic requires a generalization of a classical formula of Mertens to the Gaussian integers, which we derive from a formula of Uchiyama regarding an Euler product that involves only primes congruent to 1 (mod 4).

#### Article information

**Source**

Experiment. Math., Volume 10, Issue 2 (2001), 161-174.

**Dates**

First available in Project Euclid: 30 August 2001

**Permanent link to this document**

https://projecteuclid.org/euclid.em/999188629

**Mathematical Reviews number (MathSciNet)**

MR1837668

**Zentralblatt MATH identifier**

1045.11071

#### Citation

Renze, John; Wagon, Stan; Wick, Brian. The Gaussian Zoo. Experiment. Math. 10 (2001), no. 2, 161--174. https://projecteuclid.org/euclid.em/999188629