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1978•Communications of the ACMOpen access

A linear sieve algorithm for finding prime numbers

David Gries, Jayadev Misra

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Abstract

A new algorithm is presented for finding all primes between 2 and n . The algorithm executes in time proportional to n (assuming that multiplication of integers not larger than n can be performed in unit time). The method has the same arithmetic complexity as the algorithm presented by Mairson [6]; however, our version is perhaps simpler and more elegant. It is also easily extended to find the prime factorization of all integers between 2 and n in time proportional to n .

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What this paper is about

A new algorithm is presented for finding all primes between 2 and n . The algorithm executes in time proportional to n (assuming that multiplication of integers not larger than n can be performed in unit time). The method has the same arithmetic complexity as the algorithm presented by Mairson [6]; however, our version is perhaps simpler and more elegant. It is also easily extended to find the prime factorization of all integers between 2 and n in time proportional to n .

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Available abstract

A new algorithm is presented for finding all primes between 2 and n . The algorithm executes in time proportional to n (assuming that multiplication of integers not larger than n can be performed in unit time). The method has the same arithmetic complexity as the algorithm presented by Mairson [6]; however, our version is perhaps simpler and more elegant. It is also easily extended to find the prime factorization of all integers between 2 and n in time proportional to n .

Key concepts: Mathematics, Prime number, Prime (order theory), Algorithm, Time complexity, Prime factor, Discrete mathematics, Multiplication (music)

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