{"title":"Reducing the space used by the sieve of Eratosthenes when factoring","authors":"Samuel Hartman, Jonathan P. Sorenson","doi":"10.1016/j.ipl.2024.106537","DOIUrl":null,"url":null,"abstract":"<div><div>We present a version of the sieve of Eratosthenes that can factor all integers ≤<em>x</em> in <span><math><mi>O</mi><mo>(</mo><mi>x</mi><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>x</mi><mo>)</mo></math></span> arithmetic operations using at most <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>x</mi></mrow></msqrt><mo>/</mo><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>x</mi><mo>)</mo></math></span> bits of space. Among algorithms that take the optimal <span><math><mi>O</mi><mo>(</mo><mi>x</mi><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>x</mi><mo>)</mo></math></span> time, this new space bound is an improvement of a factor proportional to <span><math><mi>log</mi><mo></mo><mi>x</mi><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>x</mi></math></span> over the implied previous bound of <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>x</mi></mrow></msqrt><mi>log</mi><mo></mo><mi>x</mi><mo>)</mo></math></span>. We also show our algorithm performs well in practice.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Processing Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002001902400067X","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
We present a version of the sieve of Eratosthenes that can factor all integers ≤x in arithmetic operations using at most bits of space. Among algorithms that take the optimal time, this new space bound is an improvement of a factor proportional to over the implied previous bound of . We also show our algorithm performs well in practice.
期刊介绍：
Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered.
Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.
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