344-346), Xuedong Luo obtained the second extension of Eratosthenes' Sieve by removing the multiple of 2 and 3 from the original set while maintaining the same process.
In this article we further extend Eratosthenes' Sieve showing that it is possible to remove the multiples of 2,3 and 5 from the initial set without any substantial increase of comparative operations.
To extend the Eratosthenes' Sieve we need to know for any given element [Mathematical Expression Omitted] its position, the position of its square and that of the subsequent multiples of n.
As it is the case in the other extensions of Eratosthenes' Sieve the arithmetic complexity of computation and the storage requirement for this algorithm is still O(N log log N) and O(N).
Rather, both are O(N log N), because unlike Eratosthenes' Sieve, the elements of S other than the primes are used to sieve.