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Author Mairson, Harry G.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Prime number generation ♦ Balancing ♦ Preprocessing ♦ Linked list ♦ Sieve ♦ Computational complexity ♦ Number theory
Abstract Given an integer N, what is the computational complexity of finding all the primes less than N? A modified sieve of Eratosthenes using doubly linked lists yields an algorithm of OA(N) arithmetic complexity. This upper bound is shown to be equivalent to the theoretical lower bound for sieve methods without preprocessing. Use of preprocessing techniques involving space-time and additive-multiplicative tradeoffs reduces this upper bound to OA(N/log logN) and the bit complexity to OB(N logN log log logN). A storage requirement is described using OB(N logN/log logN) bits as well.
Description Affiliation: Yale Univ., New Haven, CT (Mairson, Harry G.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 20
Issue Number 9
Page Count 6
Starting Page 664
Ending Page 669


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Source: ACM Digital Library