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. Preprints2020, 2020090742. https://doi.org/10.20944/preprints202009.0742.v1
Maleki Chorei, R. Introducing Two New Sieves for Factorization Natural Odd Numbers. Preprints 2020, 2020090742. https://doi.org/10.20944/preprints202009.0742.v1
Maleki Chorei, R. Introducing Two New Sieves for Factorization Natural Odd Numbers. Preprints2020, 2020090742. https://doi.org/10.20944/preprints202009.0742.v1
APA Style
Maleki Chorei, R. (2020). Introducing Two New Sieves for Factorization Natural Odd Numbers. Preprints. https://doi.org/10.20944/preprints202009.0742.v1
Chicago/Turabian Style
Maleki Chorei, R. 2020 "Introducing Two New Sieves for Factorization Natural Odd Numbers" Preprints. https://doi.org/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.
Keywords
Prime numbers; lemmas and theorems; Fermat’s factorization method; sieve
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
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.
