The Distribution of Prime Numbers and Finding the Factor of Composite Numbers without Searching

Affiliation(s)

School of Interdisciplinary Program, Mathematics Division, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia.

School of Interdisciplinary Program, Mathematics Division, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia.

ABSTRACT

In this paper, there are 5 sections of tables represented by 5 linear sequence functions. There are two one-variable sequence functions that they are able to represent all prime numbers. The first one helps the last one to produce another three two-variable linear sequence functions. With the help of these three two-variable sequence functions, the last one, one-variable sequence function, is able to set apart all prime numbers from composite numbers. The formula shows that there are infinitely many prime numbers by applying limit to infinity. The three two-variable sequence functions help us to find the factor of all composite numbers.

In this paper, there are 5 sections of tables represented by 5 linear sequence functions. There are two one-variable sequence functions that they are able to represent all prime numbers. The first one helps the last one to produce another three two-variable linear sequence functions. With the help of these three two-variable sequence functions, the last one, one-variable sequence function, is able to set apart all prime numbers from composite numbers. The formula shows that there are infinitely many prime numbers by applying limit to infinity. The three two-variable sequence functions help us to find the factor of all composite numbers.

KEYWORDS

The n^{th} Sequence of an Arithmetic Sequence,
Number of Elements of the Set,
Sequence Functions

The n

Cite this paper

Jenber, D. (2015) The Distribution of Prime Numbers and Finding the Factor of Composite Numbers without Searching.*Advances in Pure Mathematics*, **5**, 338-352. doi: 10.4236/apm.2015.56033.

Jenber, D. (2015) The Distribution of Prime Numbers and Finding the Factor of Composite Numbers without Searching.

References

[1] (2015) http://en.wikipedia.org/wiki/Prime_number

[2] Posametier, A.S. (2003) Math Wonders to inspire Teachers and Students.

[3] Crandall, R. and Pomerance, C.B. (2005) Prime numbers: A Computational Perspective. 21.

[1] (2015) http://en.wikipedia.org/wiki/Prime_number

[2] Posametier, A.S. (2003) Math Wonders to inspire Teachers and Students.

[3] Crandall, R. and Pomerance, C.B. (2005) Prime numbers: A Computational Perspective. 21.