Finding strong pseudoprimes to several bases

DOI10.1090/S0025-5718-00-01215-1zbMath1007.11003MaRDI QIDQ2701572

Zhenxiang Zhang

Publication date: 19 February 2001

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

zbMATH Keywords

Chinese remainder theorembiquadratic residue characterscubic residue charactersRabin-Miller teststrong pseudoprimes

Mathematics Subject Classification ID

Factorization; primality (11A51) Power residues, reciprocity (11A15) Primality (11Y11)

Related Items (11)

Strong pseudoprimes to the first eight prime bases ⋮ Notes on some new kinds of pseudoprimes ⋮ Finding 𝐶₃-strong pseudoprimes ⋮ On the effectiveness of a generalization of Miller's primality theorem ⋮ Two kinds of strong pseudoprimes up to $10^{36}$ ⋮ SYLOW p-PSEUDOPRIMES TO SEVERAL BASES FOR SEVERAL PRIMES p ⋮ Finding strong pseudoprimes to several bases. II ⋮ Some new kinds of pseudoprimes ⋮ A generalised Lucasian primality test ⋮ Strong pseudoprimes to base 2 ⋮ A one-parameter quadratic-base version of the Baillie-PSW probable prime test

Uses Software

• ECPP

Cites Work

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• Probabilistic algorithm for testing primality
• Evaluation and comparison of two efficient probabilistic primality testing algorithms
• Riemann's hypothesis and tests for primality
• There are infinitely many Carmichael numbers
• Elliptic Curves and Primality Proving
• Primality Testing and Jacobi Sums
• Implementation of a new primality test
• The Pseudoprimes to 25 ⋅10 9
• On Strong Pseudoprimes to Several Bases
• Rabin-Miller Primality Test: Composite Numbers Which Pass It

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