Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-w9xp6 Total loading time: 0.358 Render date: 2022-12-06T19:45:39.720Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

The Genuine Sieve of Eratosthenes

Published online by Cambridge University Press:  01 January 2009

MELISSA E. O'NEILL*
Affiliation:
Harvey Mudd College, Claremont, CA, U.S.A (e-mail: oneill@acm.org)
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A much beloved and widely used example showing the elegance and simplicity of lazy functional programming represents itself as “The Sieve of Eratosthenes.” This paper shows that this example is not the sieve and presents an implementation that actually is.

Type
Articles
Copyright
Copyright © Cambridge University Press 2008

References

Bengelloun, S. A. (1986) An incremental primal sieve. Acta Inf. 23, 119125.CrossRefGoogle Scholar
Crandall, R. & Pomerance, C. (2001) Prime Numbers. A Computational Perspective. New York: Springer-Verlag.CrossRefGoogle Scholar
Hardy, G. H. & Wright, E. M. (1979) An Introduction to the Theory of Numbers. 5th ed.Oxford: Clarendon Press, pp. 354358.Google Scholar
Meertens, L. (2004) Calculating the Sieve of Eratosthenes. J. Funct. Prog. 14 (6), 759763.CrossRefGoogle Scholar
Paulson, L. C. (1996) ML for the Working Programmer. 2nd ed.Cambridge University Press.CrossRefGoogle Scholar
Pritchard, P. (1987) Linear prime-number sieves: A family tree. Sci. Comput. Prog. 9, 1735.CrossRefGoogle Scholar
Pritchard, P. (1994) Improved incremental prime number sieves. In Proceedings of the First International Symposium on Algorithmic Number Theory. London: Springer-Verlag, pp. 280288.CrossRefGoogle Scholar
Runciman, C. (1997) Lazy wheel sieves and spirals of primes. J. Funct. Prog. 7 (2), 219225.CrossRefGoogle Scholar
Selberg, S. (1946) An upper bound for the number of cancelled numbers in the Sieve of Eratosthenes. Det kongelige Norske videnskabers selskabs forhandlinger, Trondhjem 19 (2), 36.Google Scholar
Turner, D. A. (1975) SASL Language Manual. Technical Report CS/75/1. Department of Computational Science, University of St. Andrews.Google Scholar
Submit a response

Discussions

No Discussions have been published for this article.
You have Access
20
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The Genuine Sieve of Eratosthenes
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

The Genuine Sieve of Eratosthenes
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

The Genuine Sieve of Eratosthenes
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *