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**1 - 5**of**5**### Notes by G.J.O. Jameson

"... Recall that Fermat’s “little theorem ” says that if p is prime and a is not a multiple of p, then ap−1 ≡ 1 mod p. This theorem gives a possible way to detect primes, or more exactly, non-primes: if for some positive a ≤ n − 1, an−1 is not congruent to 1 mod n, then, by the theorem, n is ..."

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Recall that Fermat’s “little theorem ” says that if p is prime and a is not a multiple of p, then ap−1 ≡ 1 mod p. This theorem gives a possible way to detect primes, or more exactly, non-primes: if for some positive a ≤ n − 1, an−1 is not congruent to 1 mod n, then, by the theorem, n is

### 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.

### 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 ..."

Abstract
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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.