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Modern cryptography algorithms are commonly used to ensure informationsecurity. Prime numbers are needed in many asymmetric cryptography algorithms.For example, RSA algorithm selects two large prime numbers and multiplies toeach other to obtain a large composite number whose factorization is verydifficult. Producing a prime number is not an easy task as they are notdistributed regularly through integers. Primality testing algorithms are usedto determine whether a particular number is prime or composite. In this paper,an intensive survey is thoroughly conducted among the several primality testingalgorithms showing the pros and cons, the time complexity, and a brief summaryof each algorithm. Besides, an implementation of these algorithms isaccomplished using Java and Python as programming languages to evaluate theefficiency of both the algorithms and the programming languages.

Taxonomy and Practical Evaluation of Primality Testing Algorithms