Year: 2015
Type: article
Abstract: A prime sieve is an algorithm that finds the primes up to a bound $n$ . We say that a prime sieve is incremental, if it can quickly determine if $n+1$ is prime after having found all primes up to $n$ . We say a sieve is compact if it uses roughly $\sqrt{n}$ space or less. In this paper, we present two new results. – We describe the rolling sieve, a practical, incremental prime sieve that takes $O(n\log \log n)$ time and $O(\sqrt{n}\log n)$ bits of space. – We also show how to modify the sieve of Atkin and Bernstein from 2004 to obtain a sieve that is simultaneously sublinear, compact, and incremental. The second result solves an open problem given by Paul Pritchard in 1994.
Author: Jonathan P. Sorenson
Institution: Butler University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Butler University
OpenAlex ID: W1505090994