Algorithmic Number Theory

Volume 1838 of the series Lecture Notes in Computer Science pp 539-549

A Fast Algorithm for Approximately Counting Smooth Numbers

  • Jonathan P. SorensonAffiliated withComputer Science Department, Butler University

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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.