Full paper in PDF:

$%A. R. Quesada and B. van Pelt, A note on the extensions of Eratosthenes’ Sieve,
Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 1, 99–108.%$

A Note on the Extensions of Eratosthenes’
Sieve

Antonio R. QUESADA and B. VAN PELT

Department of Mathematical Sciences

University of Akron

44325-4002 Akron, OH — USA

University of Akron

44325-4002 Akron, OH — USA

ABSTRACT

Given , let denote the set of natural numbers relatively prime to the first primes. The -extension of the Sieve or Eratosthenes, recently found, provides a set of rules that govern the positions in of the multiples of the elements of . In this paper we provide an alternative approach to the -extension which yields an easier implementation in parallel processing. In addition it is shown that, with an appropriate layout of the set , the rules governing the sieving process can be made similar to those in the original sieve.

1991 Mathematics Subject Classification: 11A41, 11-04, 11Y16.