International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 539-544

On the K-th extension of the Sieve of eratosthenes

Antonio R. Quesada

Department of Mathematical Sciences, The University of Akron, Akron 44325-4002, OH, USA

Received 19 November 1993; Revised 28 March 1994

Copyright © 1995 Antonio R. Quesada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Sieve of Eratosthenes has been recently extended by excluding the multiples of 2, 3, and 5 from the initial set, and finding the additive rules that give the positions of the multiples of the remaining primes. We generalize these results. For a given k we let the initial set Sk consists of natural numbers relatively prime to the first k primes, and find the rules governing the positions of the multiples of the remaining elements.