Two Compact Incremental Prime Sieves

Authors

Jonathan P. Sorenson, Butler UniversityFollow

Document Type

Article

Publication Date

2015

Publication Title

LMS Journal of Computation and Mathematics

First Page

675

Last Page

683

DOI

https://doi.org/10.1112/S1461157015000194

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 √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(√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.

Rights

This is a pre-print version of this article. The version of record is available at Cambridge University Press.

NOTE: this version of the article is pending revision and may not reflect the changes made in the final, peer-reviewed version.

Recommended Citation

Sorenson, Jonathan P., "Two Compact Incremental Prime Sieves" LMS Journal of Computation and Mathematics / (2015): 675-683.
Available at https://digitalcommons.butler.edu/facsch_papers/968