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
Received: September 30, 1994
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.