# IJPAM: Volume 85, No. 5 (2013)

GENERATION OF PRIME NUMBERS FROM
ADVANCED SEQUENCE AND DECOMPOSITION METHODS

Brahim Belhaouari Samir1, Munwar Ali Zardari2, Youssef A. Y. Rezk3
1Mathematics Department Science College
Alfaisal University
2,3Department of Computer and Information Sciences
Universirti Teknologi PETRONAS
Bandar Seri Iskandar, 31750, Tronoh, Perak, MALAYSIA

Abstract. The generation of prime numbers cause the use of data encryption techniques, as major primal is needed for the generation of pairs of keys. This paper proposes two prime number generation methods which are based on sequence of prime numbers and decomposition of a prime number". In these proposed methods, co-prime and decomposition properties of prime number are used. By considering the co-prime property, any sequence of consecutive primes are coupled together to generate their co-prime numbers. Let n be a number which is co-prime with a sequence of m prime numbers, which can be expressed as:
n=\left ( \prod\limits_{i=1}^{m} p_{i}\right ).k+V_{mod\left ( \prod\limits_{i=1}^{m}p_{i} \right )},
where m is a sequence of prime numbers and pi be the i-th prime number, with p1=1. In the second approach i.e decomposition of prime number, the objective is to generate new prime numbers using decomposition of primes. For all integer numbers represented by X less than p2m+1 are prime numbers, it is shown in the following formula.
X\left ( i,w,r \right )=\sum\limits_{j=1}^{i}\left ( \prod\limits_{l\varepsilon I_{i}^{j}} p_{l}^{w_{i}^{d}\left ( l \right )}\left ( -1 \right)^{r_{i}^{d}(l)}\right).

Received: August 11, 2012

AMS Subject Classification: 11XX, 11YXX, 11Y11

Key Words and Phrases: prime numbers, twin primes, co-prime number, prime number decomposition.

DOI: 10.12732/ijpam.v85i5.2 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 5