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Asymptotic semismoothness probabilities
 Mathematics of computation
, 1996
"... Abstract. We call an integer semismooth with respect to y and z if each of its prime factors is ≤ y, and all but one are ≤ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(α, β)bethe asymptotic probability that a random integer n is semismooth with res ..."
Abstract

Cited by 26 (2 self)
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Abstract. We call an integer semismooth with respect to y and z if each of its prime factors is ≤ y, and all but one are ≤ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(α, β)bethe asymptotic probability that a random integer n is semismooth with respect to n β and n α. We present new recurrence relations for G and related functions. We then give numerical methods for computing G,tablesofG, and estimates for the error incurred by this asymptotic approximation. 1.
Asymptotic Semismoothness Probabilities
"... Abstract We call an integer semismooth with respect to y and z if each of its prime factors is ^ y, and all but one are ^ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(ff; fi) be the asymptotic probability that a random integer n is semismooth with ..."
Abstract
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Abstract We call an integer semismooth with respect to y and z if each of its prime factors is ^ y, and all but one are ^ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(ff; fi) be the asymptotic probability that a random integer n is semismooth with respect to nfi and nff. We present new recurrence relations for G and related functions. We then give numerical methods for computing G, tables of G, and estimates for the error incurred by this asymptotic approximation.