A space-efficient fast prime number sieve

We present a new algorithm that finds all primes up to n using at most O( n log log n ) arithmetic operations and O( n (log n log log n) ) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime nu...

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Vydáno v:Information processing letters Ročník 59; číslo 2; s. 79 - 84
Hlavní autoři: Dunten, Brian, Jones, Julie, Sorenson, Jonathan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 22.07.1996
Elsevier Science
Elsevier Sequoia S.A
Témata:
Algebra
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis of algorithms
Applied sciences
Computer science; control theory; systems
Design of algorithms
Exact sciences and technology
Information processing
Mathematical analysis
Mathematics
Number theoretic algorithms
Number theory
Prime number sieve
Prime numbers
Sciences and techniques of general use
Sieve of Eratosthenes
Studies
Theoretical computing
Design of algorithms
Analysis of algorithms
Prime number sieve
Sieve of Eratosthenes
Number theoretic algorithms
Algorithms
Arithmetic operation
Eratosthène sieve
Algorithm analysis
Prime number
ISSN:0020-0190, 1872-6119
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Popis
Shrnutí:We present a new algorithm that finds all primes up to n using at most O( n log log n ) arithmetic operations and O( n (log n log log n) ) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of Θ ( log n). In addition, we present the results of our implementations of most known prime number sieves.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0020-0190
1872-6119
DOI:10.1016/0020-0190(96)00099-3