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Approximately counting semismooth integers
An integer is -semismooth if where is an integer with
all prime divisors and is 1 or a prime . arge quantities of
semismooth integers are utilized in modern integer factoring algorithms, such
as the number field sieve, that incorporate the so-called large prime variant.
Thus, it is useful for factoring practitioners to be able to estimate the value
of , the number of -semismooth integers up to , so that
they can better set algorithm parameters and minimize running times, which
could be weeks or months on a cluster supercomputer. In this paper, we explore
several algorithms to approximate using a generalization of
Buchstab's identity with numeric integration.Comment: To appear in ISSAC 2013, Boston M
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