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**1 - 3**of**3**### unknown title

, 711

"... Abstract. Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implement ..."

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Abstract. Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implementation up to 10 24. Statistics relevant to the distribution of threeprime Carmichael numbers are given, with particular reference to the conjecture of Granville and Pomerance in [10]. 1.

### NEW POLYNOMIALS PRODUCING ABSOLUTE PSEUDOPRIMES WITH ANY NUMBER OF PRIME FACTORS

, 2007

"... Abstract. In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed as a generalization of Chernick’s result. By the si ..."

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Abstract. In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed as a generalization of Chernick’s result. By the similar method, we give another type of polynomials producing many absolute pseudoprimes. As concrete examples, we tabulate the counts of such numbers of our forms. 1.

### unknown title

, 711

"... Abstract. Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implement ..."

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Abstract. Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implementation up to 10 24. Statistics relevant to the distribution of threeprime Carmichael numbers are given, with particular reference to the conjecture of Granville and Pomerance in [10]. 1.