# A New Approach for Examining a Given Number to be a Prime Number

## Keywords:

Congruence, Collatz conjecture, Matlab programming, Prime numbers, Primality test## Abstract

Any whole number greater than 1 that is divisible only by 1 and itself, is defined as a prime number. Therefore a prime is a number that has only two factors. The chaotic nature of prime numbers in the set of integer numbers makes it important in today’s world, particularly in cryptosystems. If it was possible to determine the predictable nature of primes, the cryptosystems of the world could crash. There are a number of mathematical arguments backing the fact that it is not possible to predict the nature of prime numbers. So one can only formulate a tool for testing whether a given number is likely to be a prime number. Following the theme, here in this article, we also formulate a method to check whether a given number is a probable prime number or not. We also derive a connection between the Collatz conjecture and prime numbers.

## References

M. Dorsey and S. Zachary. “Methods of primality testing.” SMIT Undergraduate Journal of Mathematics, vol (1), 133-141, 1999.

S. Ishmukhametov and B. Mubarakov. “On practical aspects of the Miller-Rabin primality test.” Lobachevskii Journal of Mathematics, vol. (34)4, pp.304-312, 2013.

Rosenberg and Burt. “The Solovay-Strassen Primality Test.” University of Miami. Department of Computer Science. Miami, 1993.

M. Agrawal; N. Kayal; N Saxena. "PRIMES is in P" (PDF). Annals of Mathematics. vol. 160 (2), pp. 781–793, 2004.

Cohen, Henri; Lenstra, W, Hendrik., Jr. "Primality testing and Jacobi sums". Mathematics of Computation. vol. 42, (165), pp. 297–330, 1984.

L.K. Hua. “Introduction to number theory”. Springer Science & Business Media, 2012.

I.N. Herstein. “Topics in algebra”. John Wiley & Sons, 2006.

P. Honner. “The Simple Math Problem We Still Can’t Solve”. Internet: www.quantamagazine.org.html, Sep. 20, 2020 [Oct.10, 2020]

K. Hartnet. “Mathematician Proves Huge Result on ‘Dangerous’ Problem.” Internet: www.quantamagazine.org.html, Dec. 11, 2019 [May.30, 2020]

## Downloads

## Published

## How to Cite

*American Scientific Research Journal for Engineering, Technology, and Sciences*,

*88*(1), 77–90. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/7486

## Issue

## Section

## License

Authors who submit papers with this journal agree to the following terms.