The AKS algorithm successfully solved the noted problem of deterministic primality testing in polynomial time, but it was not yet suitable for the real application, thus it was improved in series. In order to further analyze the practical efficiency of currently improved versions of the AKS algorithm, one of them (called the second AKS Bernstein algorithm), which was proposed by Bernstein, was implemented by using Delphi Pascal program on PC Pentium I V/1.8 G, and its running efficiency were compared with that of other versions. For data that formerly needed tens or thousands of hours to complete the primality test with previous versions, only several seconds were required when running with the second AKS Bernstein algorithm. Thus, the conclusion that the second AKS Bernstein algorithm is better than other improved versions was got. In addition, some defects of the second AKS Bernstein algorithm were analyzed, and the suggestion that the second AKS Bernstein algorithm remains to be improved was made.
