Abstract
Let Ψ(x,y) denote the number of integers ≤ x that are composed entirely of primes bounded by y. We present an algorithm for estimating the value of Ψ(x,y) with a running time roughly proportional to \(\sqrt{y}\). Our algorithm is a modification of an algorithm by Hunter and Sorenson that is based on a theorem of Hildebrand and Tenenbaum. This previous algorithm ran in time roughly proportional to y.
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Sorenson, J.P. (2000). A Fast Algorithm for Approximately Counting Smooth Numbers. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_36
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DOI: https://doi.org/10.1007/10722028_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67695-9
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