We have known the problem of prime numbers recognition for thousands of years, but it has been considered a more theoretical problem. It was not until the twentieth century that scientists realized the importance of this problem for practical purposes as well, since cryptographic systems were designed on the basis of large prime numbers. Scientists developed randomized polynomial algorithms, which are in practice very useful and sufficient for the needs of secure cryptographic systems. There was still open question of whether there was a polynomial deterministic algorithm for testing primes. Such an algorithm was introduced in 2002 by three Indian scientists Agrawal, Kayal and Saxena.
In the thesis we examined the most known algorithms for the given problem and described the first polynomial deterministic algorithm AKS and proved it. We also presented an implementation of algorithm AKS.
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