You need to consider the wider context of your particular application. There are always pros and cons of any design decision, but their impact changes depending on the situation, so you have to think every time.
Splitting the long number into several fields makes it easier to read, especially if you choose to divide the number the same way as most of your users. You can also often validate the input as soon as the user goes to the next field, so you indicate errors earlier.
On the other hand, users rarely type long numbers like that nowadays: most of the time they just copy-paste them from whatever note-keeping solution they have chosen, in whatever format they have it there. That means that a single field, without any limit on lenght or allowed characters suddenly makes a lot of sense -- you can filter the characters out anyways (just make sure you display the final form of the number to the user at some point). There are also issues with moving the focus between fields, with browsers remembering previous values (you just have to select one number, not 4 parts of the same number then), etc.
In general, I would say that as browsers slowly become more and more usable, you should take advantage of the mechanisms they provide by using the stock solutions, and not inventing complex solutions on your own. You may be a step before them today, but in two years the browsers will catch up and your site will suck.