Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value PC is introduced here. It is closely related to the doubled p-value and has an intuitive appeal. Its use is advocated for both continuous and discrete distributions. An important advantage of this p-value is that equi...

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 “e...