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2001 The Gaussian Zoo
John Renze, Stan Wagon, Brian Wick
Experiment. Math. 10(2): 161-174 (2001).

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).

Citation

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John Renze. Stan Wagon. Brian Wick. "The Gaussian Zoo." Experiment. Math. 10 (2) 161 - 174, 2001.

Information

Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 1045.11071
MathSciNet: MR1837668

Rights: Copyright © 2001 A K Peters, Ltd.

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Vol.10 • No. 2 • 2001
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