**Category:**

Research Papers

**Sub-Category:**

Mathematics and Applied Mathematics

**Date Published:**

July 7, 2015

**Keywords:**

Sieve, Eratosthenes, Prime Numbers, Factors

**Abstract:**

This paper develops an algorithmic version of the Sieve of Eratosthenes to identify all the prime numbers up to and including any desired natural number. The method also provides for the simple calculation of Pi(N).
In addition, the primary term in the algorithm enables a new and very simple method for the determination of primality or compositeness of any number and, in the case of the latter, the factors involved, which enables these parameters to be easily determined for very large composite numbers.

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