In this study, prime numbers and primality, which IS one of the most important topics in number theory is analyzed.Subject of primality of a number has been the focus of many scientific studies and several different theories has been developed for many years. Based on these theorems, primality of large numbers has been investigated. There are also computer based algorithms to test large numbers.In this work, five different testing methods have been studied and computer programs have been developed. Best method was determined by comparing the test results from different methods.