Tracing private mobile numbers may have been a tedious task before, but with the advent of the internet, there is nothing that you cannot find. You may have been easily able to locate the regular telephone number of any person whom you needed by just flipping through the ancient yellow pages. But the same is not the case with private mobile numbers, mainly because they are well, private. Thus, you will have to go through the privacy rights (not necessarily violate) in order to locate personal information of any person. Therefore, the easily available white pages (or yellow pages) is of no use if it is a cell phone number that you are looking for. Even other similar public realm databases will prove to be useless in this regard.
So where else do you look for cell phone numbers? The internet of course (not a Private Detective if that's what you were thinking). So all that you need to do is log on to such database online, and obtain not only basic personal information like name and sex, but also something deeper like address, marital status, average income and so on. And you don't even have to limit yourself to just a single search; it can be unlimited. These online databases assure complete reliability and precision.
Now the reasons for looking up a private phone number may vary, and can range from keeping a tab on a cheating spouse, maybe getting to the root of annoying prank calls, or simply to track an old friend or colleague.