Generation of prime numbers from advanced sequence and decomposition methods

The generation of prime numbers cause the use of data encryp- tion 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 = ( Π^m _i=1 pi ) .k + V _mod(Π ^m _i=1 pi), 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 p² _m+1 are prime numbers, it is shown in the following formula. X (i,w, r) = Σⁱ _j=1 ( Π _{lεIj i}p ^{wd i (l)} l (-1)^{rd i (l)} ) .