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Building Pseudoprimes With A Large Number Of Prime Factors
, 1995
"... We extend the method due originally to Loh and Niebuhr for the generation of Carmichael numbers with a large number of prime factors to other classes of pseudoprimes, such as Williams's pseudoprimes and elliptic pseudoprimes. We exhibit also some new Dickson pseudoprimes as well as superstrong ..."
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We extend the method due originally to Loh and Niebuhr for the generation of Carmichael numbers with a large number of prime factors to other classes of pseudoprimes, such as Williams's pseudoprimes and elliptic pseudoprimes. We exhibit also some new Dickson pseudoprimes as well as superstrong Dickson pseudoprimes.
A new algorithm for constructing large Carmichael
 Ken Nakamula, Department of Mathematics and Information Sciences, Tokyo Metropolitan University, MinamiOsawa, Hachioji
, 1996
"... Abstract. We describe an algorithm for constructing Carmichael numbers N with a large number of prime factors p1,p2,...,pk. This algorithm starts with a given number Λ = lcm(p1 − 1,p2 −1,...,pk − 1), representing the value of the Carmichael function λ(N). We found Carmichael numbers with up to 11015 ..."
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Abstract. We describe an algorithm for constructing Carmichael numbers N with a large number of prime factors p1,p2,...,pk. This algorithm starts with a given number Λ = lcm(p1 − 1,p2 −1,...,pk − 1), representing the value of the Carmichael function λ(N). We found Carmichael numbers with up to 1101518 factors. 1.
Pseudoprimes: A Survey Of Recent Results
, 1992
"... this paper, we aim at presenting the most recent results achieved in the theory of pseudoprime numbers. First of all, we make a list of all pseudoprime varieties existing so far. This includes Lucaspseudoprimes and the generalization to sequences generated by integer polynomials modulo N , elliptic ..."
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this paper, we aim at presenting the most recent results achieved in the theory of pseudoprime numbers. First of all, we make a list of all pseudoprime varieties existing so far. This includes Lucaspseudoprimes and the generalization to sequences generated by integer polynomials modulo N , elliptic pseudoprimes. We discuss the making of tables and the consequences on the design of very fast primality algorithms for small numbers. Then, we describe the recent work of Alford, Granville and Pomerance, in which they prove that there
ANEWALGORITHM FOR CONSTRUCTING LARGE CARMICHAEL NUMBERS
"... Abstract. We describe an algorithm for constructing Carmichael numbers N with a large number of prime factors p1,p2,...,pk. This algorithm starts with a given number Λ = lcm(p1 − 1,p2 −1,...,pk −1), representing the value of the Carmichael function λ(N). We found Carmichael numbers with up to 110151 ..."
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Abstract. We describe an algorithm for constructing Carmichael numbers N with a large number of prime factors p1,p2,...,pk. This algorithm starts with a given number Λ = lcm(p1 − 1,p2 −1,...,pk −1), representing the value of the Carmichael function λ(N). We found Carmichael numbers with up to 1101518 factors. 1.