Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Introducing Two New Sieves for Factorization Natural Odd Numbers

Version 1 : Received: 24 September 2020 / Approved: 30 September 2020 / Online: 30 September 2020 (12:12:58 CEST)

How to cite: Maleki Chorei, R. Introducing Two New Sieves for Factorization Natural Odd Numbers. Preprints 2020, 2020090742 (doi: 10.20944/preprints202009.0742.v1). Maleki Chorei, R. Introducing Two New Sieves for Factorization Natural Odd Numbers. Preprints 2020, 2020090742 (doi: 10.20944/preprints202009.0742.v1).

Abstract

For each non-prime odd number as F=pq , if we consider m/n as an approximation for q/p and choose k=mn , then by proving some lemmas and theorems, we can compute the values of m and n. Finally, by using Fermat’s factorization method for F and 4kF as difference of two non-consecutive natural numbers, we should be able to find the values of p and q. Then we introduce two new and powerful sieves for separating composite numbers from prime numbers.

Subject Areas

Prime numbers; lemmas and theorems; Fermat’s factorization method; sieve

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