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We remark that the AKS primality testing algorithm [Annals of Mathematics 160(2), 2004] needs about 1,000,000,000 G (gigabyte) storage space for a number of1024 bits. The requirement is very hard to meet. The complexity class P whichcontains all decision problems that can be solved by a deterministic Turingmachine using a polynomial amount of computation time, is generally believed tobe ``easy". We point out that the time is estimated only in terms of the amountof arithmetic operations. It does not comprise the time for reading and writingdata on the tape in a Turing machine. The flaw makes some deterministicpolynomial time algorithms impractical, and humbles the importance of P=NPquestion.

Remarks on AKS Primality Testing Algorithm and A Flaw in the Definition of P