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