  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 of
1024 bits. The requirement is very hard to meet. The complexity class P which
contains all decision problems that can be solved by a deterministic Turing
machine using a polynomial amount of computation time, is generally believed to
be ``easy". We point out that the time is estimated only in terms of the amount
of arithmetic operations. It does not comprise the time for reading and writing
data on the tape in a Turing machine. The flaw makes some deterministic
polynomial time algorithms impractical, and humbles the importance of P=NP
question.
