International Association
for Cryptologic Research

We remark that AKS primality testing algorithm needs about 1,000,000,000 G (gigabyte) storage space for a number of 1024 bits. Such storage requirement is hard to meet in practice. To the best of our knowledge, it is impossible for current operating systems to write and read data in so huge storage space. Thus, the running time for AKS algorithm shuould not be simply estimated as usual in terms of the amount of arithmetic operations.