The most important notion about pseudo-random numbers s that they are not truly random by definition, since their relationship is exactly known. Nevertheless, pseudo-random numbers are used a lot. Their production on computers is simple and fast. On the other hand, they suffer from known and unknown defects. Various randomness tests like the Diehard battery of tests may uncover serious problems.
Many simple generators suffer from serious statistical defects.
If such numbers are used for simulations, they may lead to wrong results. Actually, there can never be a definition of a random process. If so, it would not be random, because it would obey a certain rule used to build it. Therefore, the definition of randomness is intrinsically not possible . In practice, we are left with pseudo-definitions.