Gaussian Mersenne and Eisenstein Mersenne primes

DOI10.1090/S0025-5718-10-02324-0zbMath1217.11119MaRDI QIDQ3584848

Pedro Berrizbeitia, Boris Iskra

Publication date: 30 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Eisenstein Mersenne primesGaussian Mersenne primes

Mathematics Subject Classification ID

Primality (11Y11)

Related Items (2)

Primes of the form \(x^2 + d y^2\) with \(x\equiv 0\pmod N\) or \(y\equiv 0\pmod N\) ⋮ Efficient finite groups arising in the study of relative asphericity

Cites Work

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• Effective primality tests for integers of the forms \(N=k3^ n+1\) and \(N=k2^ m3^ n+1\)
• Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers
• The Complex Sum of Divisors
• Criteria for cubic and quartic residuacity
• New Primality Criteria and Factorizations of 2 m ± 1
• Perfect ideals over the Gaussian integers
• Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 𝐴.3ⁿ±1
• Perfect Gaussian integers
• Biquadratic reciprocity and a Lucasian primality test
• On Euler's Criterion for Cubic Nonresidues

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