International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 539-544
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 we let the initial
set consists of natural numbers relatively prime to the first primes, and find the rules
governing the positions of the multiples of the remaining elements.