Full paper in PDF:
$%A. R. Quesada and B. van Pelt, A note on the extensions of Eratosthenes’ Sieve, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 1, 99108.%$

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

Received: September 30, 1994

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

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