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

## Authors

• Lourens Nicolaas Jacobus Engelbrecht Independent Researcher, 33 William Road, Pringle Bay, 7196, South Africa.

## 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.

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