Experimental Mathematics

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


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